Topological realizations of chain complexes. II. The rational case

Justin R. Smith

Vol. 138 (1989), No. 1, 169–208

DOI: 10.2140/pjm.1989.138.169

Abstract

This paper continues the study of the realizability question for chain complexes. We address the following question:

Given a group π and a ℚπ-projective chain-complex T, does there exist a topological space with fundamental group isomorphic to π whose equivariant chain complex is T?

We essentially answer this question in the affirmative in an important special case and develop a purely algebraic obstruction theory for the problem in the general case.

Mathematical Subject Classification 2000

Primary: 55U15

Secondary: 55S45

Milestones

Received: 7 September 1987

Published: 1 May 1989