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

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Publisher : Princeton University Press
ISBN 13 : 1400865166
Total Pages : 138 pages
Book Rating : 4.4/5 (8 download)

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

Download or read book The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-Manifolds. (MN-44), Volume 44 written by John W. Morgan and published by Princeton University Press. This book was released on 2014-09-08 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-manifolds

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Author :
Publisher : Princeton University Press
ISBN 13 : 9780691025971
Total Pages : 140 pages
Book Rating : 4.0/5 (259 download)

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Book Synopsis The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-manifolds by : John W. Morgan

Download or read book The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-manifolds written by John W. Morgan and published by Princeton University Press. This book was released on 1996 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

4-Manifolds

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Publisher : Oxford University Press
ISBN 13 : 0191087750
Total Pages : 280 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis 4-Manifolds by : Selman Akbulut

Download or read book 4-Manifolds written by Selman Akbulut and published by Oxford University Press. This book was released on 2016-09-08 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Smooth Four-Manifolds and Complex Surfaces

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Publisher : Springer Science & Business Media
ISBN 13 : 3662030284
Total Pages : 532 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Smooth Four-Manifolds and Complex Surfaces by : Robert Friedman

Download or read book Smooth Four-Manifolds and Complex Surfaces written by Robert Friedman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Seiberg Witten and Gromov Invariants for Symplectic 4-manifolds

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Publisher :
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.:/5 (321 download)

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Book Synopsis Seiberg Witten and Gromov Invariants for Symplectic 4-manifolds by : Clifford Taubes

Download or read book Seiberg Witten and Gromov Invariants for Symplectic 4-manifolds written by Clifford Taubes and published by . This book was released on 2005 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: On March 28-30, 1996, International Press, the National Science Foundation, and the University of California sponsored the First Annual International Press Lecture Series, held on the Irvine campus. This volume consists of four papers comprising the proof of the author's result relating the Seiberg-Witten and Gromov invariants of four manifolds.

Gauge Theory and the Topology of Four-Manifolds

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Publisher :
ISBN 13 : 9781470439033
Total Pages : 221 pages
Book Rating : 4.4/5 (39 download)

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Book Synopsis Gauge Theory and the Topology of Four-Manifolds by : Robert Friedman

Download or read book Gauge Theory and the Topology of Four-Manifolds written by Robert Friedman and published by . This book was released on 1997 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying SU(2)-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory. Gauge theory long predates Donaldson's applications of the subject to 4.

Smooth Four-Manifolds and Complex Surfaces

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Publisher :
ISBN 13 : 9783662030295
Total Pages : 536 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Smooth Four-Manifolds and Complex Surfaces by : Robert Friedman

Download or read book Smooth Four-Manifolds and Complex Surfaces written by Robert Friedman and published by . This book was released on 2014-01-15 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Notes on Seiberg-Witten Theory

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Publisher : American Mathematical Soc.
ISBN 13 : 0821821458
Total Pages : 504 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Notes on Seiberg-Witten Theory by : Liviu I. Nicolaescu

Download or read book Notes on Seiberg-Witten Theory written by Liviu I. Nicolaescu and published by American Mathematical Soc.. This book was released on 2000 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: After background on elliptic equations, Clifford algebras, Dirac operators, and Fredholm theory, chapters introduce solutions of the Seiberg-Witten equations and the group of gauge transformations, then look at algebraic surfaces. A final chapter presents in great detail a cut-and-paste technique for computing Seiberg-Witten invariants, covering elliptic equations on manifolds with cylindrical ends, finite energy monopoles on cylindrical manifolds, local and global properties of the moduli spaces of finite energy monopoles, and the process of reconstructing the space of monopoles on a 4-manifold decomposed into several parts by a hypersurface. Annotation copyrighted by Book News, Inc., Portland, OR.

Instantons and Four-Manifolds

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Publisher : Springer Science & Business Media
ISBN 13 : 1461397030
Total Pages : 212 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Instantons and Four-Manifolds by : Daniel S. Freed

Download or read book Instantons and Four-Manifolds written by Daniel S. Freed and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

The Topology of 4-Manifolds

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Publisher : Nankai Institute of Mathematics, Tianjin, P.R. China
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis The Topology of 4-Manifolds by : Robion C. Kirby

Download or read book The Topology of 4-Manifolds written by Robion C. Kirby and published by Nankai Institute of Mathematics, Tianjin, P.R. China. This book was released on 1989 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Floer Homology, Gauge Theory, and Low-Dimensional Topology

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821838457
Total Pages : 318 pages
Book Rating : 4.8/5 (384 download)

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Book Synopsis Floer Homology, Gauge Theory, and Low-Dimensional Topology by : Clay Mathematics Institute. Summer School

Download or read book Floer Homology, Gauge Theory, and Low-Dimensional Topology written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2006 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces. The use of gauge theory as a tool for studying topological properties of four-manifolds was pioneered by the fundamental work of Simon Donaldson in theearly 1980s, and was revolutionized by the introduction of the Seiberg-Witten equations in the mid-1990s. Since the birth of the subject, it has retained its close connection with symplectic topology. The analogy between these two fields of study was further underscored by Andreas Floer's constructionof an infinite-dimensional variant of Morse theory that applies in two a priori different contexts: either to define symplectic invariants for pairs of Lagrangian submanifolds of a symplectic manifold, or to define topological This volume is based on lecture courses and advanced seminars given at the 2004 Clay Mathematics Institute Summer School at the Alfred Renyi Institute of Mathematics in Budapest, Hungary. Several of the authors have added a considerable amount of additional material tothat presented at the school, and the resulting volume provides a state-of-the-art introduction to current research, covering material from Heegaard Floer homology, contact geometry, smooth four-manifold topology, and symplectic four-manifolds. Information for our distributors: Titles in this seriesare copublished with the Clay Mathematics Institute (Cambridge, MA).

Topics in Symplectic 4-manifolds

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Publisher :
ISBN 13 :
Total Pages : 144 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Topics in Symplectic 4-manifolds by : Ronald J. Stern

Download or read book Topics in Symplectic 4-manifolds written by Ronald J. Stern and published by . This book was released on 1998 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: In March 1996 the first annual IP Lecture series took place. It included ten one-hour invited lectures by prominent researchers in four-dimensional smooth and symplectic topology. This volume contains six of these lectures.

The Geometry of Four-manifolds

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Publisher :
ISBN 13 : 9781383025651
Total Pages : 0 pages
Book Rating : 4.0/5 (256 download)

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Book Synopsis The Geometry of Four-manifolds by : S. K. Donaldson

Download or read book The Geometry of Four-manifolds written by S. K. Donaldson and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Exotic Smoothness and Physics

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Publisher : World Scientific
ISBN 13 : 981024195X
Total Pages : 339 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Exotic Smoothness and Physics by : Torsten Asselmeyer-Maluga

Download or read book Exotic Smoothness and Physics written by Torsten Asselmeyer-Maluga and published by World Scientific. This book was released on 2007 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many Christians have an easier time being saved by grace than they do living in grace every day. But grace is at the center of the life God calls us to--and reflects the heart of the One who calls.These studies in Grace will help you make the connection between grace as a remote biblical concept and grace as a lifestyle--a reality you experience day in, day out. Through an unfolding study of Psalm 23, you'll learn how God--our Good Shepherd--is for you, how he longs to walk with you through temptation, sorrow, and even deep regret. You'll discover God's desire to make his joy your joy. Throughout, you'll learn how enduring, powerful, and life-affirming God's work in your life can be---and rediscover why it's called amazing grace.Leader's guide included!Grace group sessions are:Living in GraceGrace for RegretsSustaining GraceDelighting in GraceA Legacy of GraceGrace ForeverGrace to Share

Connections, Definite Forms, and Four-manifolds

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Publisher : Oxford University Press on Demand
ISBN 13 : 9780198535997
Total Pages : 131 pages
Book Rating : 4.5/5 (359 download)

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Book Synopsis Connections, Definite Forms, and Four-manifolds by : Ted Petrie

Download or read book Connections, Definite Forms, and Four-manifolds written by Ted Petrie and published by Oxford University Press on Demand. This book was released on 1990 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this book is the study of the relationship between the geometry and topology of four-manifolds. The authors adopt a topologists' perspective and present a lucid introduction to moduli space techniques, and then apply them to four-manifolds.

Grid Homology for Knots and Links

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Publisher : American Mathematical Soc.
ISBN 13 : 1470417375
Total Pages : 410 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Grid Homology for Knots and Links by : Peter S. Ozsváth

Download or read book Grid Homology for Knots and Links written by Peter S. Ozsváth and published by American Mathematical Soc.. This book was released on 2015-12-04 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a classical area of low-dimensional topology, directly connected with the theory of three-manifolds and smooth four-manifold topology. In recent years, the subject has undergone transformative changes thanks to its connections with a number of other mathematical disciplines, including gauge theory; representation theory and categorification; contact geometry; and the theory of pseudo-holomorphic curves. Starting from the combinatorial point of view on knots using their grid diagrams, this book serves as an introduction to knot theory, specifically as it relates to some of the above developments. After a brief overview of the background material in the subject, the book gives a self-contained treatment of knot Floer homology from the point of view of grid diagrams. Applications include computations of the unknotting number and slice genus of torus knots (asked first in the 1960s and settled in the 1990s), and tools to study variants of knot theory in the presence of a contact structure. Additional topics are presented to prepare readers for further study in holomorphic methods in low-dimensional topology, especially Heegaard Floer homology. The book could serve as a textbook for an advanced undergraduate or part of a graduate course in knot theory. Standard background material is sketched in the text and the appendices.

Lectures on Symplectic Geometry

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Publisher : Springer
ISBN 13 : 354045330X
Total Pages : 220 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva

Download or read book Lectures on Symplectic Geometry written by Ana Cannas da Silva and published by Springer. This book was released on 2004-10-27 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.