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Author: Andrew Ranicki
Publisher: Cambridge University Press
Published: 1992-12-10
Total Pages: 372
ISBN-13: 9780521420242
DOWNLOAD EBOOK →Assuming no previous acquaintance with surgery theory and justifying all the algebraic concepts used by their relevance to topology, Dr Ranicki explains the applications of quadratic forms to the classification of topological manifolds, in a unified algebraic framework.
Author: John M. Lee
Publisher: Springer Science & Business Media
Published: 2006-04-06
Total Pages: 395
ISBN-13: 038722727X
DOWNLOAD EBOOK →Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Author: Michael S. Weiss
Publisher: American Mathematical Soc.
Published: 2014-08-12
Total Pages: 122
ISBN-13: 147040981X
DOWNLOAD EBOOK →The structure space of a closed topological -manifold classifies bundles whose fibers are closed -manifolds equipped with a homotopy equivalence to . The authors construct a highly connected map from to a concoction of algebraic -theory and algebraic -theory spaces associated with . The construction refines the well-known surgery theoretic analysis of the block structure space of in terms of -theory.
Author: John Lee
Publisher: Springer
Published: 2013-01-25
Total Pages: 0
ISBN-13: 9781461427902
DOWNLOAD EBOOK →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.
Author: John M. Lee
Publisher: Springer Science & Business Media
Published: 2000
Total Pages: 385
ISBN-13: 9780387950266
DOWNLOAD EBOOK →In this book the author motivates what is to follow in the book by explaining the roles manifolds play in topology, geometry, complex analysis, algebra & classical mechanics with a final pass at general relativity. The book begins with the basics of general topology & gently moves to manifolds, the fundamental group, & covering spaces.
Author: Robion C. Kirby
Publisher: Princeton University Press
Published: 1977-05-21
Total Pages: 376
ISBN-13: 9780691081915
DOWNLOAD EBOOK →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.
Author: Markus Land
Publisher: Springer Nature
Published: 2021-04-21
Total Pages: 300
ISBN-13: 3030615243
DOWNLOAD EBOOK →This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects of modern pure mathematics. It treats the basics of the theory and supplies all the necessary details while leading the reader along a streamlined path from the basic definitions to more advanced results such as the very important adjoint functor theorems. The book is based on lectures given by the author on the topic. While the material itself is well-known to experts, the presentation of the material is, in parts, novel and accessible to non-experts. Exercises complement this textbook that can be used both in a classroom setting at the graduate level and as an introductory text for the interested reader.
Author: R. James Milgram
Publisher: American Mathematical Soc.
Published: 1978-12-31
Total Pages: 332
ISBN-13: 9780821867891
DOWNLOAD EBOOK →Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.
Author: Loring W. Tu
Publisher: Springer Science & Business Media
Published: 2010-10-05
Total Pages: 426
ISBN-13: 1441974008
DOWNLOAD EBOOK →Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
Author: Andrew Ranicki
Publisher: Oxford University Press
Published: 2002
Total Pages: 386
ISBN-13: 0198509243
DOWNLOAD EBOOK →This book is an introduction to surgery theory: the standard classification method for high-dimensional manifolds. It is aimed at graduate students, who have already had a basic topology course, and would now like to understand the topology of high-dimensional manifolds. This text contains entry-level accounts of the various prerequisites of both algebra and topology, including basic homotopy and homology, Poincare duality, bundles, co-bordism, embeddings, immersions, Whitehead torsion, Poincare complexes, spherical fibrations and quadratic forms and formations. While concentrating on the basic mechanics of surgery, this book includes many worked examples, useful drawings for illustration of the algebra and references for further reading.
