The total surgery obstruction revisited

Details The total surgery obstruction revisited The total surgery obstruction revisited

2011-04-27

arxiv.org/abs/1104.5092v2

Mathematics

Algebraic Topology

71 pages, revised version, section 14 substantially expanded

Scientific paper

The total surgery obstruction of a finite n-dimensional Poincare complex X is an element s(X) of a certain abelian group S_n (X) with the property that for n >= 5 we have s(X) = 0 if and only if X is homotopy equivalent to a closed n-dimensional topological manifold. The definitions of S_n (X) and s(X) and the property are due to Ranicki in a combination of results of two books and several papers. In this paper we present these definitions and a detailed proof of the main result so that they are in one place and we also add some of the details not explicitly written down in the original sources.

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