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Topological Library Characteristic Classes And Smooth Structures On Manifolds
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Book Synopsis Topological Library: Characteristic classes and smooth structures on manifolds by : Serge? Petrovich Novikov
Download or read book Topological Library: Characteristic classes and smooth structures on manifolds written by Serge? Petrovich Novikov and published by World Scientific. This book was released on 2009-10-01 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s?1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated ?singular homologies of fiber spaces.?
Book Synopsis Topological Library by : Sergeĭ Petrovich Novikov
Download or read book Topological Library written by Sergeĭ Petrovich Novikov and published by World Scientific. This book was released on 2010 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. On manifolds homeomorphic to the 7-sphere / J. Milnor -- 2. Groups of homotopy spheres. I / M. Kervaire and J. Milnor -- 3. Homotopically equivalent smooth manifolds / S.P. Novikov -- 4. Rational Pontrjagin classes. Homeomorphism and homotopy type of closed manifolds / S.P. Novikov -- 5. On manifolds with free abelian fundamental group and their applications (Pontrjagin classes, smooth structures, high-dimensional knots) / S.P. Novikov -- 6. Stable homeomorphisms and the annulus conjecture / R. Kirby
Book Synopsis Topological Library - Part 2: Characteristic Classes And Smooth Structures On Manifolds by : Serguei Petrovich Novikov
Download or read book Topological Library - Part 2: Characteristic Classes And Smooth Structures On Manifolds written by Serguei Petrovich Novikov and published by World Scientific. This book was released on 2009-10-07 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of a three-volume set collecting the original and now-classic works in topology written during the 1950s-1960s. The original methods and constructions from these works are properly documented for the first time in this book. No existing book covers the beautiful ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated “singular homologies of fiber spaces.”
Download or read book Topological library written by and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Piecewise Linear Structures on Topological Manifolds by : Yuli B. Rudyak
Download or read book Piecewise Linear Structures on Topological Manifolds written by Yuli B. Rudyak and published by World Scientific Publishing Company. This book was released on 2016 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of triangulations of topological spaces has always been at the root of geometric topology. Among the most studied triangulations are piecewise linear triangulations of high-dimensional topological manifolds. Their study culminated in the late 1960s-early 1970s in a complete classification in the work of Kirby and Siebenmann. It is this classification that we discuss in this book, including the celebrated Hauptvermutung and Triangulation Conjecture.The goal of this book is to provide a readable and well-organized exposition of the subject, which would be suitable for advanced graduate students in topology. An exposition like this is currently lacking.
Book Synopsis Characteristic Classes and Smooth Structures on Manifolds by :
Download or read book Characteristic Classes and Smooth Structures on Manifolds written by and published by . This book was released on 2010 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 1994-03-10 with total page 536 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 An Introduction to Smooth Manifolds by : Manjusha Majumdar
Download or read book An Introduction to Smooth Manifolds written by Manjusha Majumdar and published by Springer Nature. This book was released on 2023-06-01 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Targeted to graduate students of mathematics, this book discusses major topics like the Lie group in the study of smooth manifolds. It is said that mathematics can be learned by solving problems and not only by just reading it. To serve this purpose, this book contains a sufficient number of examples and exercises after each section in every chapter. Some of the exercises are routine ones for the general understanding of topics. The book also contains hints to difficult exercises. Answers to all exercises are given at the end of each section. It also provides proofs of all theorems in a lucid manner. The only pre-requisites are good working knowledge of point-set topology and linear algebra.
Book Synopsis Smooth S1 Manifolds by : Wolf Iberkleid
Download or read book Smooth S1 Manifolds written by Wolf Iberkleid and published by Lecture Notes in Mathematics. This book was released on 1976-11 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometry and Topology of Manifolds by : Hans U. Boden
Download or read book Geometry and Topology of Manifolds written by Hans U. Boden and published by American Mathematical Soc.. This book was released on 2005 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expository papers that give an up-to-date account of recent developments and open problems in the geometry and topology of manifolds, along with several research articles that present new results appearing in published form for the first time. The unifying theme is the problem of understanding manifolds in low dimensions, notably in dimensions three and four, and the techniques include algebraic topology, surgery theory, Donaldson and Seiberg-Witten gauge theory,Heegaard Floer homology, contact and symplectic geometry, and Gromov-Witten invariants. The articles collected for this volume were contributed by participants of the Conference "Geometry and Topology of Manifolds" held at McMaster University on May 14-18, 2004 and are representative of the manyexcellent talks delivered at the conference.
Book Synopsis Introduction to Smooth Manifolds by : John M. Lee
Download or read book Introduction to Smooth Manifolds written by John M. Lee and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why
Book Synopsis Smoothings of Piecewise Linear Manifolds. (AM-80), Volume 80 by : Morris W. Hirsch
Download or read book Smoothings of Piecewise Linear Manifolds. (AM-80), Volume 80 written by Morris W. Hirsch and published by Princeton University Press. This book was released on 2016-03-02 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure.
Book Synopsis Introduction to Topological Manifolds by : John Lee
Download or read book Introduction to Topological Manifolds written by John Lee and published by Springer Science & Business Media. This book was released on 2010-12-25 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.
Book Synopsis Topology of Manifolds by : Raymond Louis Wilder
Download or read book Topology of Manifolds written by Raymond Louis Wilder and published by American Mathematical Soc.. This book was released on 1979 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a standard in this area of mathematics and is invaluable for historical background.
Book Synopsis Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 by : Robion C. Kirby
Download or read book Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 written by Robion C. Kirby and published by Princeton University Press. This book was released on 2016-03-02 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Book Synopsis Smoothings of Piecewise Linear Manifolds by : Morris W. Hirsch
Download or read book Smoothings of Piecewise Linear Manifolds written by Morris W. Hirsch and published by Princeton University Press. This book was released on 1974-10-21 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of the authors is to examine the relationship between piecewise linear structure and differential structure: a relationship, they assert, that can be understood as a homotopy obstruction theory, and, hence, can be studied by using the traditional techniques of algebraic topology. Thus the book attacks the problem of existence and classification (up to isotopy) of differential structures compatible with a given combinatorial structure on a manifold. The problem is completely "solved" in the sense that it is reduced to standard problems of algebraic topology. The first part of the book is purely geometrical; it proves that every smoothing of the product of a manifold M and an interval is derived from an essentially unique smoothing of M. In the second part this result is used to translate the classification of smoothings into the problem of putting a linear structure on the tangent microbundle of M. This in turn is converted to the homotopy problem of classifying maps from M into a certain space PL/O. The set of equivalence classes of smoothings on M is given a natural abelian group structure.
