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The Topological Classification of Stratified Spaces : Chicago Lectures in Mathematics - Shmuel Weinberger

The Topological Classification of Stratified Spaces

Chicago Lectures in Mathematics

Paperback Published: 1st January 1994
ISBN: 9780226885674
Number Of Pages: 298

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This book provides the theory for stratified spaces, along with important examples and applications, that is analogous to the surgery theory for manifolds. In the first expository account of this field, Weinberger provides topologists with a new way of looking at the classification theory of singular spaces with his original results.
Divided into three parts, the book begins with an overview of modern high-dimensional manifold theory. Rather than including complete proofs of all theorems, Weinberger demonstrates key constructions, gives convenient formulations, and shows the usefulness of the technology. Part II offers the parallel theory for stratified spaces. Here, the topological category is most completely developed using the methods of "controlled topology." Many examples illustrating the topological invariance and noninvariance of obstructions and characteristic classes are provided. Applications for embeddings and immersions of manifolds, for the geometry of group actions, for algebraic varieties, and for rigidity theorems are found in Part III.
This volume will be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry.

Manifold theory
Algebraic K-theory and topology
Surgery theory
Spacification and functoriality
General theory
Definitions and examples
Classification of stratified spaces
Transverse stratified classification
PT category
Controlled topology
Proof of main theorems in topology
Applications and illustrations
Manifolds and embedding theory revisited
Supernormal spaces and varieties
Group actions
Rigidity conjectures
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780226885674
ISBN-10: 0226885674
Series: Chicago Lectures in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 298
Published: 1st January 1994
Publisher: The University of Chicago Press
Country of Publication: US
Dimensions (cm): 27.4 x 15.4  x 1.91
Weight (kg): 0.42

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