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The Topological Classification of Stratified Spaces (Paperback, New)
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The Topological Classification of Stratified Spaces (Paperback, New)
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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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