The Topological Classification of Stratified Spaces (Chicago Lectures in Mathematics)

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9780226885674: The Topological Classification of Stratified Spaces (Chicago Lectures in Mathematics)
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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.

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9780226885667: The Topological Classification of Stratified Spaces (Chicago Lectures in Mathematics)

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ISBN 10:  0226885666 ISBN 13:  9780226885667
Publisher: University of Chicago Press, 1995
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Book Description The University of Chicago Press, United States, 1995. Paperback. Condition: New. New. Language: English. Brand new Book. This text 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 2 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 3.This volume should be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry. Seller Inventory # AAH9780226885674

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Book Description The University of Chicago Press, United States, 1995. Paperback. Condition: New. New. Language: English . Brand New Book. This text 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 2 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 3. This volume should be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry. Seller Inventory # AAH9780226885674

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Book Description The University of Chicago Press, United States, 1995. Paperback. Condition: New. New. Language: English. Brand new Book. This text 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 2 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 3.This volume should be of interest to topologists, as well as mathematicians in other fields such as differential geometry, operator theory, and algebraic geometry. Seller Inventory # BTE9780226885674

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