Local Surgery and the Exact Sequence of a Localization for Wall Groups
William Pardon
Jan 1977 · American Mathematical Society: Memoirs of the American Mathematical Society Book 196 · American Mathematical Soc.
Ebook
171
Pages
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About this ebook
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.
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