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Gauge Theory And The Topology Of Four Manifolds
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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 American Mathematical Soc.. This book was released on 1998 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is part of the IAS/Park City Mathematics series and focuses on gauge theory and the topology of four-manifolds.
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
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 Oxford University Press. This book was released on 1997 with total page 464 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.
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.
Book Synopsis The Wild World of 4-Manifolds by : Alexandru Scorpan
Download or read book The Wild World of 4-Manifolds written by Alexandru Scorpan and published by American Mathematical Soc.. This book was released on 2005-05-10 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Theory of Gauge Fields in Four Dimensions by : H. Blaine Lawson
Download or read book The Theory of Gauge Fields in Four Dimensions written by H. Blaine Lawson and published by American Mathematical Soc.. This book was released on 1985 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an examination of the work of Simon Donaldson. This book offers foundation work in gauge theory (Uhlenbeck, Taubes, Atiyah, Hitchin, Singer, et al.) which underlies Donaldson's work. It is suitable for geometric topologists and differential geometers.
Book Synopsis 4-Manifolds and Kirby Calculus by : Robert E. Gompf
Download or read book 4-Manifolds and Kirby Calculus written by Robert E. Gompf and published by American Mathematical Soc.. This book was released on 1999 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author :Clay Mathematics Institute. Summer School Publisher :American Mathematical Soc. ISBN 13 :9780821838457 Total Pages :318 pages Book Rating :4.8/5 (384 download)
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).
Book Synopsis Fields Medallists' Lectures by : Michael Atiyah
Download or read book Fields Medallists' Lectures written by Michael Atiyah and published by World Scientific. This book was released on 1997-10-13 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics - and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.A list of Fields Medallists and their contributions provides a bird's eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from 22 Fields Medallists and so provides a highly interesting and varied picture.The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.The Fields Medallists' Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.
Book Synopsis Seiberg Witten Gauge Theory by : Matilde Marcolli
Download or read book Seiberg Witten Gauge Theory written by Matilde Marcolli and published by Springer. This book was released on 1999-12-15 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Four-Manifold Theory by : Cameron Gordon
Download or read book Four-Manifold Theory written by Cameron Gordon and published by American Mathematical Soc.. This book was released on 1984 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the proceedings of the Summer Research Conference on 4-manifolds held at Durham, New Hampshire, July 1982, under the auspices of the American Mathematical Society and National Science Foundation.
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 Springer. This book was released on 2006-11-14 with total page 114 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.
Book Synopsis Floer Homology Groups in Yang-Mills Theory by : S. K. Donaldson
Download or read book Floer Homology Groups in Yang-Mills Theory written by S. K. Donaldson and published by Cambridge University Press. This book was released on 2002-01-10 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of Floer homology was one of the most striking developments in differential geometry. It yields rigorously defined invariants which can be viewed as homology groups of infinite-dimensional cycles. The ideas led to great advances in the areas of low-dimensional topology and symplectic geometry and are intimately related to developments in Quantum Field Theory. The first half of this book gives a thorough account of Floer's construction in the context of gauge theory over 3 and 4-dimensional manifolds. The second half works out some further technical developments of the theory, and the final chapter outlines some research developments for the future - including a discussion of the appearance of modular forms in the theory. The scope of the material in this book means that it will appeal to graduate students as well as those on the frontiers of the subject.
Book Synopsis Mathematical Gauge Theory by : Mark J.D. Hamilton
Download or read book Mathematical Gauge Theory written by Mark J.D. Hamilton and published by Springer. This book was released on 2017-12-06 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix.
Book Synopsis Monopoles and Three-Manifolds by : Peter Kronheimer
Download or read book Monopoles and Three-Manifolds written by Peter Kronheimer and published by . This book was released on 2007-12-20 with total page 796 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2007 book provides a comprehensive treatment of Floer homology, based on the Seiberg-Witten equations. Suitable for beginning graduate students and researchers in the field, this book provides a full discussion of a central part of the study of the topology of manifolds.
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.
Book Synopsis Topological Quantum Field Theory and Four Manifolds by : Jose Labastida
Download or read book Topological Quantum Field Theory and Four Manifolds written by Jose Labastida and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
