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Topological realizations of chain complexes 1. the general theory
Journal article   Peer reviewed

Topological realizations of chain complexes 1. the general theory

Justin R. Smith
Topology and its applications, v 22(3)
Apr 1986

Abstract

Secondary 55M99 Primary 55S45
This paper studies the following question: Given a group π, and a projective Zπ-chain complex C, does there exist a topological space with a fundamental group π and with the property that the chain-complex of its universal cover is chain-homotopy equivalent to C? This is generalization of the Steenrod Problem. In the Steenrod Problem (proposed by Steenrod in 1960) the chain complex was a projective resolution of a Zπ-module. The present paper develops an obstruction theory for the existence of topological realizations of a chain-complex, algebraically classifies these realizations (if the obstructions vanish), and proves that rational chain-complexes are always stably realizable.

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Mathematics
Mathematics, Applied
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