Spaces of PL manifolds and categories of simple maps [[electronic resource] /] / Friedhelm Waldhausen, Bjørn Jahren and John Rognes

• Autore: Waldhausen Friedhelm <1938->
• 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
• ISBN: 1-4008-4652-8; 1-299-05144-8
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910779468903321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of Mathematics Studies