|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910453158003321 |
|
|
Autore |
Waldhausen Friedhelm <1938-> |
|
|
Titolo |
Spaces of PL manifolds and categories of simple maps [[electronic resource] /] / Friedhelm Waldhausen, Bjørn Jahren and John Rognes |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Princeton, : Princeton University Press, 2013 |
|
|
|
|
|
|
|
ISBN |
|
1-4008-4652-8 |
1-299-05144-8 |
|
|
|
|
|
|
|
|
Edizione |
[Course Book] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (193 p.) |
|
|
|
|
|
|
Collana |
|
Annals of Mathematics Studies ; ; 210 |
Annals of mathematics studies ; ; no. 186 |
|
|
|
|
|
|
|
|
Altri autori (Persone) |
|
JahrenBjørn <1945-> |
RognesJohn |
|
|
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Piecewise linear topology |
Mappings (Mathematics) |
Electronic books. |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
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 |
|
|
|
|