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Spaces of PL Manifolds and Categories of Simple Maps
Engelsk Paperback
Spaces of PL Manifolds and Categories of Simple Maps
Engelsk Paperback

811 kr
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Om denne bog

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.

Product detaljer
Sprog:
Engelsk
Sider:
192
ISBN-13:
9780691157764
Indbinding:
Paperback
Udgave:
ISBN-10:
0691157766
Udg. Dato:
28 apr 2013
Længde:
10mm
Bredde:
234mm
Højde:
158mm
Forlag:
Princeton University Press
Oplagsdato:
28 apr 2013
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