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The Homotopy Category Of Simply Connected 4 Manifolds
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Book Synopsis The Homotopy Category of Simply Connected 4-Manifolds by : Professor Hans-Joachim Baues
Download or read book The Homotopy Category of Simply Connected 4-Manifolds written by Professor Hans-Joachim Baues and published by . This book was released on 2014-02-19 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy of 4-manifolds for researchers and graduate students.
Book Synopsis The Homotopy Category of Simply Connected 4-manifolds by : Hans J. Baues
Download or read book The Homotopy Category of Simply Connected 4-manifolds written by Hans J. Baues and published by . This book was released on 2003 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy of 4-manifolds for researchers and graduate students.
Book Synopsis The Homotopy Category of Simply Connected 4-manifolds: category T[Gamma] and an algebraic model of CW(2,4) by : Hans J. Baues
Download or read book The Homotopy Category of Simply Connected 4-manifolds: category T[Gamma] and an algebraic model of CW(2,4) written by Hans J. Baues and published by . This book was released on 2003 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy of 4-manifolds for researchers and graduate students.
Book Synopsis The Homotopy Category of Simply Connected 4-Manifolds by : Hans J. Baues
Download or read book The Homotopy Category of Simply Connected 4-Manifolds written by Hans J. Baues and published by Cambridge University Press. This book was released on 2003-04-03 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy of 4-manifolds for researchers and graduate students.
Book Synopsis Surgery on Simply-Connected Manifolds by : William Browder
Download or read book Surgery on Simply-Connected Manifolds written by William Browder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exposition of the technique of surgery on simply-connected smooth manifolds. Systematic study of differentiable manifolds using these ideas was begun by Milnor [45] and Wallace [68] and developed extensively in the last ten years. It is now possible to give a reasonably complete theory of simply-connected manifolds of dimension ~ 5 using this approach and that is what I will try to begin here. The emphasis has been placed on stating and proving the general results necessary to apply this method in various contexts. In Chapter II, these results are stated, and then applications are given to characterizing the homotopy type of differentiable manifolds and classifying manifolds within a given homotopy type. This theory was first extensively developed in Kervaire and Milnor [34] in the case of homotopy spheres, globalized by S. P. Novikov [49] and the author [6] for closed 1-connected manifolds, and extended to the bounded case by Wall [65] and Golo [23]. The thesis of Sullivan [62] reformed the theory in an elegant way in terms of classifying spaces.
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 The Homotopy Category of Simply Connected 4-manifolds: splitting of the linear extension TL by : Hans J. Baues
Download or read book The Homotopy Category of Simply Connected 4-manifolds: splitting of the linear extension TL written by Hans J. Baues and published by . This book was released on 2003 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy of 4-manifolds for researchers and graduate students.
Book Synopsis The Homotopy Category of Simply Connected 4-manifolds: Quadratic chain complexes and algebraic models of tracks by : Hans J. Baues
Download or read book The Homotopy Category of Simply Connected 4-manifolds: Quadratic chain complexes and algebraic models of tracks written by Hans J. Baues and published by . This book was released on 2003 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy of 4-manifolds for researchers and graduate students.
Book Synopsis Surgery on Simply-connected Manifolds by : William Browder
Download or read book Surgery on Simply-connected Manifolds written by William Browder and published by Springer. This book was released on 1972 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the h-Cobordism Theorem by : John Milnor
Download or read book Lectures on the h-Cobordism Theorem written by John Milnor and published by Princeton University Press. This book was released on 2015-12-08 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Society. This book was released on 2022-01-26 with total page 614 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 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 Topology of 4-Manifolds (PMS-39), Volume 39 by : Michael H. Freedman
Download or read book Topology of 4-Manifolds (PMS-39), Volume 39 written by Michael H. Freedman and published by Princeton University Press. This book was released on 2014-07-14 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Surgery on Compact Manifolds by : Charles Terence Clegg Wall
Download or read book Surgery on Compact Manifolds written by Charles Terence Clegg Wall and published by American Mathematical Soc.. This book was released on 1999 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The publication of this book in 1970 marked the culmination of a period in the history of the topology of manifolds. This edition, based on the original text, is supplemented by notes on subsequent developments and updated references and commentaries.
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.
Download or read book Surgery Theory written by Wolfgang Lück and published by Springer Nature. This book was released on 2024 with total page 956 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological rigidity. The book also offers a detailed description of Ranicki's chain complex version, complete with a proof of its equivalence to the classical approach developed by Browder, Novikov, Sullivan, and Wall. This book has been written for learning surgery theory and includes numerous exercises. With full proofs and detailed explanations, it also provides an invaluable reference for working mathematicians. Each chapter has been designed to be largely self-contained and includes a guide to help readers navigate the material, making the book highly suitable for lecture courses, seminars, and reading courses.
Author :Robert Friedman, John W. Morgan Publisher :American Mathematical Soc. ISBN 13 :9780821886861 Total Pages :236 pages Book Rating :4.8/5 (868 download)
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 and published by American Mathematical Soc.. This book was released on with total page 236 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.
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