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Spaces of PL Manifolds and Categories of Simple Maps (AM-186), Paperback / softback Book

Spaces of PL Manifolds and Categories of Simple Maps (AM-186) Paperback / softback

Part of the Annals of Mathematics Studies series

Description

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.

Information

  • Format: Paperback / softback
  • Pages: 192 pages, 5 line illus.
  • Publisher: Princeton University Press
  • Publication Date:
  • Category: Functional analysis & transforms
  • ISBN: 9780691157764

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