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Author : Zoltán Szabó
Release : 1994
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis On the Smooth Structures of Elliptic Surfaces and Irreducible Four-manifolds by : Zoltán Szabó
Download or read book On the Smooth Structures of Elliptic Surfaces and Irreducible Four-manifolds written by Zoltán Szabó. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert Friedman
Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 284/5 ( reviews)
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. This book was released on 2013-03-09. 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.
Author : Robert Friedman, John W. Morgan
Release :
Genre : Four-manifolds (Topology).
Kind : eBook
Book Rating : 861/5 ( reviews)
Book Synopsis Gauge Theory and the Topology of Four-Manifolds by : Robert Friedman, John W. Morgan
Download or read book Gauge Theory and the Topology of Four-Manifolds written by Robert Friedman, John W. Morgan. This book was released on . 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.
Author : Alexandru Scorpan
Release : 2005-05-10
Genre : Mathematics
Kind : eBook
Book Rating : 494/5 ( reviews)
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. This book was released on 2005-05-10. 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.
Author : Robert Friedman
Release : 1998
Genre : Mathematics
Kind : eBook
Book Rating : 916/5 ( reviews)
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. This book was released on 1998. 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.
