LEADER 03483nam 2200721 a 450 001 9910453158003321 005 20200520144314.0 010 $a1-4008-4652-8 010 $a1-299-05144-8 024 7 $a10.1515/9781400846528 035 $a(CKB)2550000000996711 035 $a(EBL)1114887 035 $a(OCoLC)828077867 035 $a(SSID)ssj0000822546 035 $a(PQKBManifestationID)11442046 035 $a(PQKBTitleCode)TC0000822546 035 $a(PQKBWorkID)10760684 035 $a(PQKB)10049062 035 $a(MiAaPQ)EBC1114887 035 $a(StDuBDS)EDZ0001756468 035 $a(DE-B1597)453494 035 $a(OCoLC)933516592 035 $a(OCoLC)990531966 035 $a(DE-B1597)9781400846528 035 $a(Au-PeEL)EBL1114887 035 $a(CaPaEBR)ebr10652016 035 $a(CaONFJC)MIL436394 035 $a(EXLCZ)992550000000996711 100 $a20121220d2013 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpaces of PL manifolds and categories of simple maps$b[electronic resource] /$fFriedhelm Waldhausen, Bjørn Jahren and John Rognes 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$d2013 215 $a1 online resource (193 p.) 225 0 $aAnnals of Mathematics Studies ;$v210 225 0$aAnnals of mathematics studies ;$vno. 186 300 $aDescription based upon print version of record. 311 $a0-691-15775-8 311 $a0-691-15776-6 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tIntroduction --$t1. The stable parametrized h-cobordism theorem --$t2. On simple maps --$t3. The non-manifold part --$t4. The manifold part --$tBibliography --$tSymbols --$tIndex 330 $aSince its introduction by Friedhelm Waldhausen in the 1970's, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing Waldhausen's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a "desingularization," improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections. 410 0$aAnnals of Mathematics Studies 606 $aPiecewise linear topology 606 $aMappings (Mathematics) 608 $aElectronic books. 615 0$aPiecewise linear topology. 615 0$aMappings (Mathematics) 676 $a514/.22 700 $aWaldhausen$b Friedhelm$f1938-$01050034 701 $aJahren$b Bjørn$f1945-$01050035 701 $aRognes$b John$0521348 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910453158003321 996 $aSpaces of PL manifolds and categories of simple maps$92479504 997 $aUNINA