4 Manifolds

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The Wild World of 4-Manifolds

Alexandru Scorpan
The Wild World of 4 Manifolds Book PDF

Author : Alexandru Scorpan
Publisher : American Mathematical Society
Page : 614 pages
File Size : 40,5 Mb
Release : 2022-01-26
Category : Mathematics
ISBN : 9781470468613

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The Wild World of 4-Manifolds by Alexandru Scorpan Pdf

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.

The Geometry of Four-manifolds

S. K. Donaldson,P. B. Kronheimer
The Geometry of Four manifolds Book PDF

Author : S. K. Donaldson,P. B. Kronheimer
Publisher : Oxford University Press
Page : 464 pages
File Size : 49,6 Mb
Release : 1997
Category : Language Arts & Disciplines
ISBN : 0198502699

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The Geometry of Four-manifolds by S. K. Donaldson,P. B. Kronheimer Pdf

This text provides an accessible account to the modern study of the geometry of four-manifolds. Prerequisites are a firm grounding in differential topology and geometry, as may be gained from the first year of a graduate course.

The Topology of 4-Manifolds

Robion C. Kirby
The Topology of 4 Manifolds Book PDF

Author : Robion C. Kirby
Publisher : Springer
Page : 114 pages
File Size : 55,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540461715

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The Topology of 4-Manifolds by Robion C. Kirby Pdf

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.

4-manifolds

Selman Akbulut
4 manifolds Book PDF

Author : Selman Akbulut
Publisher : Oxford University Press
Page : 275 pages
File Size : 49,8 Mb
Release : 2016
Category : Mathematics
ISBN : 9780198784869

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4-manifolds by Selman Akbulut Pdf

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.

Instantons and Four-Manifolds

Daniel S. Freed,Karen K. Uhlenbeck
Instantons and Four Manifolds Book PDF

Author : Daniel S. Freed,Karen K. Uhlenbeck
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397038

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Instantons and Four-Manifolds by Daniel S. Freed,Karen K. Uhlenbeck Pdf

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

4-Manifolds and Kirby Calculus

Robert E. Gompf,András I. Stipsicz
4 Manifolds and Kirby Calculus Book PDF

Author : Robert E. Gompf,András I. Stipsicz
Publisher : American Mathematical Society
Page : 576 pages
File Size : 44,7 Mb
Release : 2023-08-10
Category : Mathematics
ISBN : 9781470474553

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4-Manifolds and Kirby Calculus by Robert E. Gompf,András I. Stipsicz Pdf

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

Smooth Four-Manifolds and Complex Surfaces

Robert Friedman,John W. Morgan
Smooth Four Manifolds and Complex Surfaces Book PDF

Author : Robert Friedman,John W. Morgan
Publisher : Springer Science & Business Media
Page : 532 pages
File Size : 42,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662030288

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Smooth Four-Manifolds and Complex Surfaces by Robert Friedman,John W. Morgan Pdf

In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.

Topological Quantum Field Theory and Four Manifolds

Jose Labastida,Marcos Marino
Topological Quantum Field Theory and Four Manifolds Book PDF

Author : Jose Labastida,Marcos Marino
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 40,7 Mb
Release : 2007-07-18
Category : Science
ISBN : 9781402031779

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Topological Quantum Field Theory and Four Manifolds by Jose Labastida,Marcos Marino Pdf

The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.

Topology of 4-Manifolds (PMS-39), Volume 39

Michael H. Freedman,Frank Quinn
Topology of 4 Manifolds PMS 39 Volume 39 Book PDF

Author : Michael H. Freedman,Frank Quinn
Publisher : Princeton University Press
Page : 268 pages
File Size : 54,6 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400861064

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Topology of 4-Manifolds (PMS-39), Volume 39 by Michael H. Freedman,Frank Quinn Pdf

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.

4-Manifolds and Kirby Calculus

Robert E. Gompf,András Stipsicz
4 Manifolds and Kirby Calculus Book PDF

Author : Robert E. Gompf,András Stipsicz
Publisher : American Mathematical Soc.
Page : 576 pages
File Size : 53,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821809945

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4-Manifolds and Kirby Calculus by Robert E. Gompf,András Stipsicz Pdf

Presents an exposition of Kirby calculus, or handle body theory on 4-manifolds. This book includes such topics as branched coverings and the geography of complex surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces.

The Wild World of 4-Manifolds

Alexandru Scorpan
The Wild World of 4 Manifolds Book PDF

Author : Alexandru Scorpan
Publisher : American Mathematical Soc.
Page : 642 pages
File Size : 41,6 Mb
Release : 2005-05-10
Category : Mathematics
ISBN : 9780821837498

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The Wild World of 4-Manifolds by Alexandru Scorpan Pdf

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.

The Algebraic Characterization of Geometric 4-Manifolds

J. A. Hillman
The Algebraic Characterization of Geometric 4 Manifolds Book PDF

Author : J. A. Hillman
Publisher : Cambridge University Press
Page : 184 pages
File Size : 53,6 Mb
Release : 1994-02-03
Category : Mathematics
ISBN : 9780521467780

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The Algebraic Characterization of Geometric 4-Manifolds by J. A. Hillman Pdf

This book describes work on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel-Whitney classes. Using techniques from homological group theory, the theory of 3-manifolds and topological surgery, infrasolvmanifolds are characterized up to homeomorphism, and surface bundles are characterized up to simple homotopy equivalence. Non-orientable cases are also considered wherever possible, and in the final chapter the results obtained earlier are applied to 2-knots and complex analytic surfaces.

The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44

John W. Morgan
The Seiberg Witten Equations and Applications to the Topology of Smooth Four Manifolds MN 44 Volume 44 Book PDF

Author : John W. Morgan
Publisher : Princeton University Press
Page : 138 pages
File Size : 55,8 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400865161

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The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 by John W. Morgan Pdf

The recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.

Gauge Theory and the Topology of Four-Manifolds

Robert Friedman,John W. Morgan
Gauge Theory and the Topology of Four Manifolds Book PDF

Author : Robert Friedman,John W. Morgan
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 47,5 Mb
Release : 1998
Category : Four-manifolds (Topology).
ISBN : 9780821805916

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Gauge Theory and the Topology of Four-Manifolds by Robert Friedman,John W. Morgan Pdf

This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.

An Introduction to Manifolds

Loring W. Tu
An Introduction to Manifolds Book PDF

Author : Loring W. Tu
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 48,7 Mb
Release : 2010-10-05
Category : Mathematics
ISBN : 9781441974006

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An Introduction to Manifolds by Loring W. Tu Pdf

Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.