Screen LibrarySpaces of pl manifolds and categories of simple maps (am-186) /
Since its introduction by Friedhelm Waldhausen in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book pre...
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| Main Authors: | |
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| Corporate Authors: | |
| Group Author: | ; |
| Published: |
Princeton University Press,
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| Publisher Address: | Princeton, N.J. : |
| Publication Dates: |
[2013] ©2013 |
| Literature type: | eBook |
| Language: | English |
| Series: |
Annals of mathematics studies
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| Subjects: | |
| Online Access: |
http://dx.doi.org/10.1515/9781400846528 http://www.degruyter.com/doc/cover/9781400846528.jpg |
| Summary: |
Since its introduction by Friedhelm Waldhausen in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing Waldhausen's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a "desingularization," improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections. |
| Carrier Form: | 1 online resource(192pages) : illustrations. |
| ISBN: | 9781400846528 |
| Index Number: | QA613 |
| CLC: | O189 |
| Contents: |
Frontmatter -- Contents -- Introduction -- 1. The stable parametrized h-cobordism theorem -- 2. On simple maps -- 3. The non-manifold part -- 4. The manifold part -- Bibliography -- Symbols -- Index. |