{"product_id":"9781400847587","title":"Spaces of PL Manifolds and Categories of Simple Maps (AM-186)","description":"\u003cp\u003eSince 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.\u003c\/p\u003e  \u003cp\u003e 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.\u003c\/p\u003e  \u003cp\u003e 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.\u003c\/p\u003e","brand":"Princeton University Press","offers":[{"title":"Default Title","offer_id":47137865236720,"sku":"9781400847587","price":84.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781400847587_p0.jpg?v=1763714221","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781400847587","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}