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Algebraic L-theory and Topological Manifolds

1992-12-10 Mathematics
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Release : 1992-12-10
Genre : Mathematics
Kind : eBook
Book Rating : 242/5 ( reviews)

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Book Synopsis Algebraic L-theory and Topological Manifolds by : Andrew Ranicki

Download or read book Algebraic L-theory and Topological Manifolds written by Andrew Ranicki. This book was released on 1992-12-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Topological Manifolds

2006-04-06 Mathematics
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Release : 2006-04-06
Genre : Mathematics
Kind : eBook
Book Rating : 27X/5 ( reviews)

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Book Synopsis Introduction to Topological Manifolds by : John M. Lee

Download or read book Introduction to Topological Manifolds written by John M. Lee. This book was released on 2006-04-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Topology

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 221/5 ( reviews)

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Book Synopsis Algebraic Topology by : Edwin H. Spanier

Download or read book Algebraic Topology written by Edwin H. Spanier. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

An Introduction to Manifolds

2010-10-05 Mathematics
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Release : 2010-10-05
Genre : Mathematics
Kind : eBook
Book Rating : 008/5 ( reviews)

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Book Synopsis An Introduction to Manifolds by : Loring W. Tu

Download or read book An Introduction to Manifolds written by Loring W. Tu. This book was released on 2010-10-05. Available in PDF, EPUB and Kindle. Book excerpt: 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'.

Algebraic and Geometric Surgery

2002 Mathematics
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Release : 2002
Genre : Mathematics
Kind : eBook
Book Rating : 240/5 ( reviews)

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Book Synopsis Algebraic and Geometric Surgery by : Andrew Ranicki

Download or read book Algebraic and Geometric Surgery written by Andrew Ranicki. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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