Spaces of PL Manifolds and Categories of Simple Maps (AM-186) / / Bjørn Jahren, John Rognes, Friedhelm Waldhausen.
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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Superior document: | Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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VerfasserIn: | |
Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2013] ©2013 |
Year of Publication: | 2013 |
Edition: | Course Book |
Language: | English |
Series: | Annals of Mathematics Studies ;
186 |
Online Access: | |
Physical Description: | 1 online resource (192 p.) :; 5 line illus. |
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Other title: | 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 |
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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. |
Format: | Mode of access: Internet via World Wide Web. |
ISBN: | 9781400846528 9783110494914 9783110442502 |
DOI: | 10.1515/9781400846528?locatt=mode:legacy |
Access: | restricted access |
Hierarchical level: | Monograph |
Statement of Responsibility: | Bjørn Jahren, John Rognes, Friedhelm Waldhausen. |