Journal article
Topological realizations of chain complexes 1. the general theory
Topology and its applications, v 22(3)
Apr 1986
Featured in Collection : UN Sustainable Development Goals @ Drexel
Abstract
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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Details
- Title
- Topological realizations of chain complexes 1. the general theory
- Creators
- Justin R. Smith - Drexel University
- Publication Details
- Topology and its applications, v 22(3)
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- [Retired Faculty]
- Web of Science ID
- WOS:A1986C876600009
- Scopus ID
- 2-s2.0-46149142430
- Other Identifier
- 991019173799904721
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- Web of Science research areas
- Mathematics
- Mathematics, Applied