000			02124cam a2200277 i 4500
001			17569061
003			ISI Library, Kolkata
005			20140930121902.0
008			121220s2013 nju b 001 0 eng
020			_a9780691157764 (pbk. : acidfree paper)
040			_aISI Library
082	0	0	_a514.22 _223 _bW163
100	1		_aWaldhausen, Friedhelm.
245	1	0	_aSpaces of PL manifolds and categories of simple maps / _cFriedhelm Waldhausen, Bjorn Jahren, and John Rognes.
260			_aPrinceton; _aOxford : _bPrinceton University Press, _cc2013.
300			_a184 p. : _bill. ; _c24 cm.
490			_aAnnals of mathematics studies ; _vno 186
504			_aIncludes bibliographical references (pages 175-178) and index.
505			_aIntroduction: 1. The stable parametrized h-cobordism theorem -- 2. On simple maps -- 3. The non-manifold part -- 4. The manifold part...
520			_a"Since its introduction by Friedhelm Waldhausen in the 1970s, 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."--Publisher's website.
650		0	_aPiecewise linear topology.
650		0	_aMappings (Mathematics).
700	1		_aJahren, Bjorn.
700	1		_aRognes, John.
942			_2ddc _cBK
999			_c415307 _d415307