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035   $a(DE-B1597)9781400846528
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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 /$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)
610   $aCAT Whitehead space.
610   $aCAT manifold.
610   $aEuclidean neighborhood retract.
610   $aEuclidean polyhedra.
610   $aPL Serre fibration.
610   $aPL Whitehead space.
610   $aPL homeomorphism.
610   $aPL manifold.
610   $aQuillen's Theorem A.
610   $aQuillen's Theorem B.
610   $aabsolute neighborhood retract.
610   $aalgebraic K-theory of spaces.
610   $aalgebraic K-theory.
610   $aapproximate lifting property.
610   $acofibration.
610   $adegeneracy operator.
610   $adesingularization.
610   $afinite simplicial set.
610   $ah-cobordism theorem.
610   $ahomotopy equivalence.
610   $ahomotopy fiber sequence.
610   $ahorn.
610   $amanifold space.
610   $amanifold.
610   $an-manifolds.
610   $anormal subdivision.
610   $apolyhedral realization.
610   $aq-simplex.
610   $areduced mapping cylinder.
610   $asimple map.
610   $asimplicial set.
610   $aspace.
610   $astabilization map.
610   $astable parametrized h-cobordism theorem.
610   $atangent microbundle.
610   $athickening.
610   $atriangulation.
610   $aweak homotopy equivalence.
610   $a?ech homotopy type.
615  0$aPiecewise linear topology.
615  0$aMappings (Mathematics)
676   $a514/.22
686   $aSI 830$2rvk
700   $aWaldhausen$b Friedhelm$f1938-$01686918
701   $aJahren$b Bjørn$f1945-$01686919
701   $aRognes$b John$0521348
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910813541203321
996   $aSpaces of PL manifolds and categories of simple maps$94060010
997   $aUNINA