Author : William Pardon
Publisher : American Mathematical Soc.
ISBN 13 : 0821821962
Total Pages : 187 pages
Book Rating : 4.8/5 (218 download)
Book Synopsis Local Surgery and the Exact Sequence of a Localization for Wall Groups by : William Pardon
Download or read book Local Surgery and the Exact Sequence of a Localization for Wall Groups written by William Pardon and published by American Mathematical Soc.. This book was released on 1977 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the monograph under consideration here the author develops the geometry of the situation, for any [lowercase Greek]Pi. The main tool is the notion of "a local surgery on a conglomerate Moore space'', which is a sequence of surgeries on a normal map [script]f such that each of the maps in the trace ([italic]g;[script]f,[script]fʹ):([italic]N;M,Mʹ) [right arrow]→[italic]X is a rational homotopy equivalence. It is possible to perform local surgery below the middle dimension to make an n-dimensional rational homotopy equivalence [([italic]n−2)/2]-connected, and to prove a local [lowercase Greek]Pi −[lowercase Greek]Pi theorem, so that the global local surgery obstruction is the Witt class of the linking form on the remaining kernel torsion modules. This brief summary belies the technical difficulties which have to be overcome in the process, particularly the geometric intersection theory of local surgery.
