Spaces of PL manifolds and categories of simple maps [[electronic resource] /] / Friedhelm Waldhausen, Bjørn Jahren and John Rognes
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| Autore: |
Waldhausen Friedhelm <1938->
|
| Titolo: |
Spaces of PL manifolds and categories of simple maps [[electronic resource] /] / Friedhelm Waldhausen, Bjørn Jahren and John Rognes
|
| Pubblicazione: | Princeton, : Princeton University Press, 2013 |
| Edizione: | Course Book |
| Descrizione fisica: | 1 online resource (193 p.) |
| Disciplina: | 514/.22 |
| Soggetto topico: | Piecewise linear topology |
| Mappings (Mathematics) | |
| Soggetto genere / forma: | Electronic books. |
| Altri autori: |
JahrenBjørn <1945->
RognesJohn
|
| Note generali: | Description based upon print version of record. |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | 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 |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Spaces of PL manifolds and categories of simple maps |
| ISBN: | 1-4008-4652-8 |
| 1-299-05144-8 | |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910453158003321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Annals of Mathematics Studies