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Record Nr. |
UNINA9910813541203321 |
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Autore |
Waldhausen Friedhelm <1938-> |
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Titolo |
Spaces of PL manifolds and categories of simple maps / / Friedhelm Waldhausen, Bjørn Jahren and John Rognes |
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Pubbl/distr/stampa |
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Princeton, : Princeton University Press, 2013 |
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ISBN |
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1-4008-4652-8 |
1-299-05144-8 |
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Edizione |
[Course Book] |
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Descrizione fisica |
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1 online resource (193 p.) |
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Collana |
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Annals of Mathematics Studies ; ; 210 |
Annals of mathematics studies ; ; no. 186 |
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Classificazione |
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Altri autori (Persone) |
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JahrenBjørn <1945-> |
RognesJohn |
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Disciplina |
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Soggetti |
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Piecewise linear topology |
Mappings (Mathematics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Front matter -- 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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Sommario/riassunto |
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Since its introduction by Friedhelm Waldhausen in the 1970's, 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. |
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