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[null,"1.","Record Nr.",null,"UNINA9910453158003321"]
[null,null,"Autore",null,"Waldhausen Friedhelm <1938->"]
[null,null,"Titolo",null,"Spaces of PL manifolds and categories of simple maps [[electronic resource] /] / Friedhelm Waldhausen, Bjørn Jahren and John Rognes"]
[null,null,"Pubbl/distr/stampa",null,"Princeton, : Princeton University Press, 2013"]
[null,null,"ISBN",null,"1-4008-4652-8"]
[{"$nulls":4},"1-299-05144-8"]
[null,null,"Edizione",null,"[Course Book]"]
[null,null,"Descrizione fisica",null,"1 online resource (193 p.)"]
[null,null,"Collana",null,"Annals of Mathematics Studies ; ; 210"]
[{"$nulls":4},"Annals of mathematics studies ; ; no. 186"]
[null,null,"Disciplina",null,"514/.22"]
[null,null,"Soggetti",null,"Piecewise linear topology"]
[{"$nulls":4},"Mappings (Mathematics)"]
[{"$nulls":4},"Electronic books."]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"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"]
[null,null,null,"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."]