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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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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 non controllato: | CAT Whitehead space |
CAT manifold | |
Euclidean neighborhood retract | |
Euclidean polyhedra | |
PL Serre fibration | |
PL Whitehead space | |
PL homeomorphism | |
PL manifold | |
Quillen's Theorem A. | |
Quillen's Theorem B. | |
absolute neighborhood retract | |
algebraic K-theory of spaces | |
algebraic K-theory | |
approximate lifting property | |
cofibration | |
degeneracy operator | |
desingularization | |
finite simplicial set | |
h-cobordism theorem | |
homotopy equivalence | |
homotopy fiber sequence | |
horn | |
manifold space | |
manifold | |
n-manifolds | |
normal subdivision | |
polyhedral realization | |
q-simplex | |
reduced mapping cylinder | |
simple map | |
simplicial set | |
space | |
stabilization map | |
stable parametrized h-cobordism theorem | |
tangent microbundle | |
thickening | |
triangulation | |
weak homotopy equivalence | |
Čech homotopy type | |
Classificazione: | SI 830 |
Altri autori: |
JahrenBjørn <1945->
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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.: | 9910813541203321 |
Lo trovi qui: | Univ. Federico II |
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