Topology of 4-Manifolds (PMS-39)

Author: Michael H. Freedman,Frank Quinn

Publisher: Princeton University Press

ISBN: 1400861063

Category: Mathematics

Page: 268

View: 8138

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One of the great achievements of contemporary mathematics is the new understanding of four dimensions. Michael Freedman and Frank Quinn have been the principals in the geometric and topological development of this subject, proving the Poincar and Annulus conjectures respectively. Recognition for this work includes the award of the Fields Medal of the International Congress of Mathematicians to Freedman in 1986. In Topology of 4-Manifolds these authors have collaborated to give a complete and accessible account of the current state of knowledge in this field. The basic material has been considerably simplified from the original publications, and should be accessible to most graduate students. The advanced material goes well beyond the literature; nearly one-third of the book is new. This work is indispensable for any topologist whose work includes four dimensions. It is a valuable reference for geometers and physicists who need an awareness of the topological side of the field. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The Wild World of 4-manifolds

Author: Alexandru Scorpan

Publisher: American Mathematical Soc.

ISBN: 0821837494

Category: Mathematics

Page: 609

View: 6798

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What a wonderful book! I strongly recommend this book to anyone, especially graduate students, interested in getting a sense of 4-manifolds. --MAA Reviews The book gives an excellent overview of 4-manifolds, with many figures and historical notes. Graduate students, nonexperts, and experts alike will enjoy browsing through it. -- Robion C. Kirby, University of California, Berkeley This book offers a panorama of the topology of simply connected smooth manifolds of dimension four. Dimension four is unlike any other dimension; it is large enough to have room for wild things to happen, but small enough so that there is no room to undo the wildness. For example, only manifolds of dimension four can exhibit infinitely many distinct smooth structures. Indeed, their topology remains the least understood today. To put things in context, the book starts with a survey of higher dimensions and of topological 4-manifolds. In the second part, the main invariant of a 4-manifold--the intersection form--and its interaction with the topology of the manifold are investigated. In the third part, as an important source of examples, complex surfaces are reviewed. In the final fourth part of the book, gauge theory is presented; this differential-geometric method has brought to light how unwieldy smooth 4-manifolds truly are, and while bringing new insights, has raised more questions than answers. The structure of the book is modular, organized into a main track of about two hundred pages, augmented by extensive notes at the end of each chapter, where many extra details, proofs and developments are presented. To help the reader, the text is peppered with over 250 illustrations and has an extensive index.

4-Manifolds

Author: Selman Akbulut

Publisher: Oxford University Press

ISBN: 0191087769

Category: Mathematics

Page: 280

View: 6735

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This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut. The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the proofs. The book contains a hundred colour illustrations to demonstrate the ideas rather than providing long-winded and potentially unclear explanations. Key results have been selected that relate to the material discussed and the author has provided examples of how to analyse them with the techniques developed in earlier chapters.

The Topology of 4-Manifolds

Author: Robion C. Kirby

Publisher: Springer

ISBN: 354046171X

Category: Mathematics

Page: 112

View: 1515

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This book presents the classical theorems about simply connected smooth 4-manifolds: intersection forms and homotopy type, oriented and spin bordism, the index theorem, Wall's diffeomorphisms and h-cobordism, and Rohlin's theorem. Most of the proofs are new or are returbishings of post proofs; all are geometric and make us of handlebody theory. There is a new proof of Rohlin's theorem using spin structures. There is an introduction to Casson handles and Freedman's work including a chapter of unpublished proofs on exotic R4's. The reader needs an understanding of smooth manifolds and characteristic classes in low dimensions. The book should be useful to beginning researchers in 4-manifolds.

Instantons and Four-Manifolds

Author: Daniel S. Freed,Karen K. Uhlenbeck

Publisher: Springer Science & Business Media

ISBN: 1461397030

Category: Mathematics

Page: 194

View: 3234

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From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate... The book is filled with insightful remarks, proofs, and contributions that have never before appeared in print. For anyone attempting to understand the work of Donaldson and the applications of gauge theories to four-dimensional topology, the book is a must." #Science#1 "I would strongly advise the graduate student or working mathematician who wishes to learn the analytic aspects of this subject to begin with Freed and Uhlenbeck's book." #Bulletin of the American Mathematical Society#2

Essays on Fourier Analysis in Honor of Elias M. Stein (PMS-42)

Author: Charles Fefferman,Robert Fefferman,Stephen Wainger

Publisher: Princeton University Press

ISBN: 1400852943

Category: Mathematics

Page: 396

View: 3381

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This book contains the lectures presented at a conference held at Princeton University in May 1991 in honor of Elias M. Stein's sixtieth birthday. The lectures deal with Fourier analysis and its applications. The contributors to the volume are W. Beckner, A. Boggess, J. Bourgain, A. Carbery, M. Christ, R. R. Coifman, S. Dobyinsky, C. Fefferman, R. Fefferman, Y. Han, D. Jerison, P. W. Jones, C. Kenig, Y. Meyer, A. Nagel, D. H. Phong, J. Vance, S. Wainger, D. Watson, G. Weiss, V. Wickerhauser, and T. H. Wolff. The topics of the lectures are: conformally invariant inequalities, oscillatory integrals, analytic hypoellipticity, wavelets, the work of E. M. Stein, elliptic non-smooth PDE, nodal sets of eigenfunctions, removable sets for Sobolev spaces in the plane, nonlinear dispersive equations, bilinear operators and renormalization, holomorphic functions on wedges, singular Radon and related transforms, Hilbert transforms and maximal functions on curves, Besov and related function spaces on spaces of homogeneous type, and counterexamples with harmonic gradients in Euclidean space. Originally published in 1995. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Leonhard Euler

Mathematical Genius in the Enlightenment

Author: Ronald S. Calinger

Publisher: Princeton University Press

ISBN: 1400866634

Category: Biography & Autobiography

Page: 696

View: 3254

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This is the first full-scale biography of Leonhard Euler (1707–83), one of the greatest mathematicians and theoretical physicists of all time. In this comprehensive and authoritative account, Ronald Calinger connects the story of Euler's eventful life to the astonishing achievements that place him in the company of Archimedes, Newton, and Gauss. Drawing chiefly on Euler’s massive published works and correspondence, which fill more than eighty volumes so far, this biography sets Euler’s work in its multilayered context—personal, intellectual, institutional, political, cultural, religious, and social. It is a story of nearly incessant accomplishment, from Euler’s fundamental contributions to almost every area of pure and applied mathematics—especially calculus, number theory, notation, optics, and celestial, rational, and fluid mechanics—to his advancements in shipbuilding, telescopes, ballistics, cartography, chronology, and music theory. The narrative takes the reader from Euler’s childhood and education in Basel through his first period in St. Petersburg, 1727–41, where he gained a European reputation by solving the Basel problem and systematically developing analytical mechanics. Invited to Berlin by Frederick II, Euler published his famous Introductio in analysin infinitorum, devised continuum mechanics, and proposed a pulse theory of light. Returning to St. Petersburg in 1766, he created the analytical calculus of variations, developed the most precise lunar theory of the time that supported Newton’s dynamics, and published the best-selling Letters to a German Princess—all despite eye problems that ended in near-total blindness. In telling the remarkable story of Euler and how his achievements brought pan-European distinction to the Petersburg and Berlin academies of sciences, the book also demonstrates with new depth and detail the central role of mathematics in the Enlightenment. Some images inside the book are unavailable due to digital copyright restrictions.

Operations Research for Unmanned Systems

Author: John Q. Dickmann, Jr.

Publisher: John Wiley & Sons

ISBN: 1118918940

Category: Technology & Engineering

Page: 352

View: 370

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The first edited volume addressing analysis for unmanned vehicles, with focus on operations research rather than engineering • The editors have a unique combination of extensive operational experience and technical expertise • Chapters address a wide-ranging set of examples, domains and applications • Accessible to a general readership and also informative for experts

Welcome to the Universe

An Astrophysical Tour

Author: Neil deGrasse Tyson,Michael A. Strauss,J. Richard Gott

Publisher: Princeton University Press

ISBN: 1400883229

Category: Science

Page: 480

View: 1707

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A NEW YORK TIMES BESTSELLER Welcome to the Universe is a personal guided tour of the cosmos by three of today's leading astrophysicists. Inspired by the enormously popular introductory astronomy course that Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott taught together at Princeton, this book covers it all—from planets, stars, and galaxies to black holes, wormholes, and time travel. Describing the latest discoveries in astrophysics, the informative and entertaining narrative propels you from our home solar system to the outermost frontiers of space. How do stars live and die? Why did Pluto lose its planetary status? What are the prospects of intelligent life elsewhere in the universe? How did the universe begin? Why is it expanding and why is its expansion accelerating? Is our universe alone or part of an infinite multiverse? Answering these and many other questions, the authors open your eyes to the wonders of the cosmos, sharing their knowledge of how the universe works. Breathtaking in scope and stunningly illustrated throughout, Welcome to the Universe is for those who hunger for insights into our evolving universe that only world-class astrophysicists can provide.

Machine Dreams

Economics Becomes a Cyborg Science

Author: Philip Mirowski

Publisher: Cambridge University Press

ISBN: 9780521775267

Category: Business & Economics

Page: 655

View: 6005

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This was the first cross-over book into the history of science written by an historian of economics. It shows how 'history of technology' can be integrated with the history of economic ideas. The analysis combines Cold War history with the history of postwar economics in America and later elsewhere, revealing that the Pax Americana had much to do with abstruse and formal doctrines such as linear programming and game theory. It links the literature on 'cyborg' to economics, an element missing in literature to date. The treatment further calls into question the idea that economics has been immune to postmodern currents, arguing that neoclassical economics has participated in the deconstruction of the integral 'self'. Finally, it argues for an alliance of computational and institutional themes, and challenges the widespread impression that there is nothing else besides American neoclassical economic theory left standing after the demise of Marxism.

Violent Neoliberalism

Development, Discourse, and Dispossession in Cambodia

Author: S. Springer

Publisher: Springer

ISBN: 1137485337

Category: Social Science

Page: 219

View: 7640

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Violent Neoliberalism explores the complex unfolding relationship between neoliberalism and violence. Employing a series of theoretical dialogues on development, discourse and dispossession Cambodia, this study sheds significant empirical light on the vicious implications of free market ideology and practice.

Data Engineering and Management

Second International Conference, ICDEM 2010, Tiruchirappalli, India, July 29-31, 2010. Revised Selected Papers

Author: Rajkumar Kannan,Frederic Andres

Publisher: Springer

ISBN: 3642278728

Category: Computers

Page: 356

View: 9758

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This book constitutes the thoroughly refereed post-conference proceedings of the Second International Conference on Data Engineering and Management, ICDEM 2010, held in Tiruchirappalli, India, in July 2010. The 46 revised full papers presented together with 1 keynote paper and 2 tutorial papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on Digital Library; Knowledge and Mulsemedia; Data Management and Knowledge Extraction; Natural Language Processing; Workshop on Data Mining with Graphs and Matrices.

3D Radiative Transfer in Cloudy Atmospheres

Author: Alexander Marshak,Anthony Davis

Publisher: Springer Science & Business Media

ISBN: 3540285199

Category: Science

Page: 686

View: 7014

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Developments in three-dimensional cloud radiation over the past few decades are assessed and distilled into this contributed volume. Chapters are authored by subject-matter experts who address a broad audience of graduate students, researchers, and anyone interested in cloud-radiation processes in the solar and infrared spectral regions. After two introductory chapters and a section on the fundamental physics and computational techniques, the volume extensively treats two main application areas: the impact of clouds on the Earth's radiation budget, which is an essential aspect of climate modeling; and remote observation of clouds, especially with the advanced sensors on current and future satellite missions.

Riemannian Manifolds

An Introduction to Curvature

Author: John M. Lee

Publisher: Springer Science & Business Media

ISBN: 0387227261

Category: Mathematics

Page: 226

View: 8191

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This text focuses on developing an intimate acquaintance with the geometric meaning of curvature and thereby introduces and demonstrates all the main technical tools needed for a more advanced course on Riemannian manifolds. It covers proving the four most fundamental theorems relating curvature and topology: the Gauss-Bonnet Theorem, the Cartan-Hadamard Theorem, Bonnet’s Theorem, and a special case of the Cartan-Ambrose-Hicks Theorem.

Expanding the Frontiers of Visual Analytics and Visualization

Author: John Dill,Rae Earnshaw,David Kasik,John Vince,Pak Chung Wong

Publisher: Springer Science & Business Media

ISBN: 1447128044

Category: Computers

Page: 531

View: 6087

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The field of computer graphics combines display hardware, software, and interactive techniques in order to display and interact with data generated by applications. Visualization is concerned with exploring data and information graphically in such a way as to gain information from the data and determine significance. Visual analytics is the science of analytical reasoning facilitated by interactive visual interfaces. Expanding the Frontiers of Visual Analytics and Visualization provides a review of the state of the art in computer graphics, visualization, and visual analytics by researchers and developers who are closely involved in pioneering the latest advances in the field. It is a unique presentation of multi-disciplinary aspects in visualization and visual analytics, architecture and displays, augmented reality, the use of color, user interfaces and cognitive aspects, and technology transfer. It provides readers with insights into the latest developments in areas such as new displays and new display processors, new collaboration technologies, the role of visual, multimedia, and multimodal user interfaces, visual analysis at extreme scale, and adaptive visualization.

Lectures on the H-Cobordism Theorem

Author: John Milnor

Publisher: Princeton University Press

ISBN: 1400878055

Category: Mathematics

Page: 124

View: 9134

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These lectures provide students and specialists with preliminary and valuable information from university courses and seminars in mathematics. This set gives new proof of the h-cobordism theorem that is different from the original proof presented by S. Smale. Originally published in 1965. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Physical Relativity

Space-time Structure from a Dynamical Perspective

Author: Harvey R. Brown

Publisher: Oxford University Press on Demand

ISBN: 0199275831

Category: Science

Page: 225

View: 1331

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Physical Relativity explores the nature of the distinction at the heart of Einstein's 1905 formulation of his special theory of relativity: that between kinematics and dynamics. Einstein himself became increasingly uncomfortable with this distinction, and with the limitations of what he called the 'principle theory' approach inspired by the logic of thermodynamics. A handful of physicists and philosophers have over the last century likewise expressed doubts about Einstein'streatment of the relativistic behaviour of rigid bodies and clocks in motion in the kinematical part of his great paper, and suggested that the dynamical understanding of length contraction and time dilation intimated by the immediate precursors of Einstein is more fundamental. Harvey Brown both examines andextends these arguments (which support a more 'constructive' approach to relativistic effects in Einstein's terminology), after giving a careful analysis of key features of the pre-history of relativity theory. He argues furthermore that the geometrization of the theory by Minkowski in 1908 brought illumination, but not a causal explanation of relativistic effects. Finally, Brown tries to show that the dynamical interpretation of special relativity defended in the book is consistent with therole this theory must play as a limiting case of Einstein's 1915 theory of gravity: the general theory of relativity.Appearing in the centennial year of Einstein's celebrated paper on special relativity, Physical Relativity is an unusual, critical examination of the way Einstein formulated his theory. It also examines in detail certain specific historical and conceptual issues that have long given rise to debate in both special and general relativity theory, such as the conventionality of simultaneity, the principle of general covariance, and the consistency or otherwise of the special theory withquantum mechanics. Harvey Brown' s new interpretation of relativity theory will interest anyone working on these central topics in modern physics.

4-manifolds and Kirby Calculus

Author: Robert E. Gompf,András Stipsicz

Publisher: American Mathematical Soc.

ISBN: 0821809946

Category: Mathematics

Page: 558

View: 4116

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Since the early 1980s, there has been an explosive growth in 4-manifold theory, particularly due to the influx of interest and ideas from gauge theory and algebraic geometry. This book offers an exposition of the subject from the topological point of view. It bridges the gap to other disciplines and presents classical but important topological techniques that have not previously appeared in the literature. Part I of the text presents the basics of the theory at the second-year graduate level and offers an overview of current research. Part II is devoted to an exposition of Kirby calculus, or handlebody theory on 4-manifolds. It is both elementary and comprehensive. Part III offers in-depth treatments of a broad range of topics from current 4-manifold research. Topics include branched coverings and the geography of complex surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces. The authors present many important applications. The text is supplemented with over 300 illustrations and numerous exercises, with solutions given in the book. I greatly recommend this wonderful book to any researcher in 4-manifold topology for the novel ideas, techniques, constructions, and computations on the topic, presented in a very fascinating way. I think really that every student, mathematician, and researcher interested in 4-manifold topology, should own a copy of this beautiful book. --Zentralblatt MATH This book gives an excellent introduction into the theory of 4-manifolds and can be strongly recommended to beginners in this field ... carefully and clearly written; the authors have evidently paid great attention to the presentation of the material ... contains many really pretty and interesting examples and a great number of exercises; the final chapter is then devoted to solutions of some of these ... this type of presentation makes the subject more attractive and its study easier. --European Mathematical Society Newsletter

Complex Algebraic Surfaces

Author: Arnaud Beauville

Publisher: Cambridge University Press

ISBN: 9780521498425

Category: Mathematics

Page: 132

View: 9307

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The classification of algebraic surfaces is an intricate and fascinating branch of mathematics, developed over more than a century and still an active area of research today. In this book, Professor Beauville gives a lucid and concise account of the subject, expressed simply in the language of modern topology and sheaf theory, and accessible to any budding geometer. A chapter on preliminary material ensures that this volume is self-contained while the exercises succeed both in giving the flavor of the classical subject, and in equipping the reader with the techniques needed for research. The book is aimed at graduate students in geometry and topology.