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The total surgery obstruction revisited

2011/04/27 by Philipp Kuehl, Kuehl, Philipp, Tibor Macko +3
Biochemistry, Genetics and Molecular Biology · Medicine · #(57P10) #57R67 #Algebraic Topology (math.AT) #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Ophthalmology and Eye Disorders #Soft tissue tumor case studies

paper · pdf · doi:10.48550/arxiv.1104.5092

openalex publication_date 2011/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The total surgery obstruction of a finite n-dimensional Poincare complex X is an element s(X) of a certain abelian group Sn (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 Sn (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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