03483nam 2200721 a 450 991045315800332120200520144314.01-4008-4652-81-299-05144-810.1515/9781400846528(CKB)2550000000996711(EBL)1114887(OCoLC)828077867(SSID)ssj0000822546(PQKBManifestationID)11442046(PQKBTitleCode)TC0000822546(PQKBWorkID)10760684(PQKB)10049062(MiAaPQ)EBC1114887(StDuBDS)EDZ0001756468(DE-B1597)453494(OCoLC)933516592(OCoLC)990531966(DE-B1597)9781400846528(Au-PeEL)EBL1114887(CaPaEBR)ebr10652016(CaONFJC)MIL436394(EXLCZ)99255000000099671120121220d2013 uy 0engurcn|||||||||txtccrSpaces of PL manifolds and categories of simple maps[electronic resource] /Friedhelm Waldhausen, Bjørn Jahren and John RognesCourse BookPrinceton Princeton University Press20131 online resource (193 p.)Annals of Mathematics Studies ;210Annals of mathematics studies ;no. 186Description based upon print version of record.0-691-15775-8 0-691-15776-6 Includes bibliographical references and index.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 --IndexSince 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.Annals of Mathematics StudiesPiecewise linear topologyMappings (Mathematics)Electronic books.Piecewise linear topology.Mappings (Mathematics)514/.22Waldhausen Friedhelm1938-1050034Jahren Bjørn1945-1050035Rognes John521348MiAaPQMiAaPQMiAaPQBOOK9910453158003321Spaces of PL manifolds and categories of simple maps2479504UNINA