Click Here to Download: https://ouo.io/E76C3R Spaces of PL Manifolds and Categories of Simple Maps (AM-186) By: Friedhelm Waldhausen; Bjørn Jahren; John Rognes Publisher: Princeton University Press Print ISBN: 9780691157764, 0691157766 eText ISBN: 9781400846528, 1400846528 Pages: 192 Copyright year: 2013 Format: PDF Available from $ 84.00 USD SKU 9781400846528 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. Additional ISBNs 9780691157757, 9780691157764, 0691157758, 0691157766, 9780691157757, 0691157758
