Spaces of PL manifolds and categories of simple maps / Friedhelm Waldhausen, Bjorn Jahren, and John Rognes.
Material type:
- 9780691157764 (pbk. : acidfree paper)
- 514.22 23 W163
Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
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Books | ISI Library, Kolkata | 514.22 W163 (Browse shelf(Opens below)) | Available | 135289 |
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514.22 G548 Geometrical combinatorial topology | 514.22 L858 Course in topological combinatorics | 514.22 P818 Foundations of combinatorial topology | 514.22 W163 Spaces of PL manifolds and categories of simple maps / | 514.223 Topology of stiefel manifolds | 514.223 B435 Complex manifolds | 514.223 B462 Branched standard spines of 3-manifolds |
Includes bibliographical references (pages 175-178) and index.
Introduction:
1. The stable parametrized h-cobordism theorem --
2. On simple maps --
3. The non-manifold part --
4. The manifold part...
"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.
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