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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-> Visualizza persona
Titolo: Spaces of PL manifolds and categories of simple maps [[electronic resource] /] / Friedhelm Waldhausen, Bjørn Jahren and John Rognes Visualizza cluster
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->  
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  Visualizza cluster
ISBN: 1-4008-4652-8
1-299-05144-8
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910779468903321
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Serie: Annals of Mathematics Studies