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On the twisted cobar construction

Published online by Cambridge University Press:  01 March 1997

HANS-JOACHIM BAUES  and
ANDREW TONKS
HANS-JOACHIM BAUES
Affiliation:
Max-Planck-Institut für Mathematik, Gottfried-Claren-Straße 26, 53225 Bonn, Germany
ANDREW TONKS
Affiliation:
Max-Planck-Institut für Mathematik, Gottfried-Claren-Straße 26, 53225 Bonn, Germany
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Abstract

The classical cobar construction ΩC for a coalgebra C (first introduced by Adams[1]) is an important algebraic concept motivated by the singular chain complex of a loop space ΩX. If X is a 1-reduced simplicial set with realization |X|, Adams proved that there is a natural isomorphism of homology groups

formula here

where C(X) si the coalgebra given by th chain complex on X abd tge Alexander-Whitney diagonal. Here the homology has coefficients in an abelian group A. The purpose of this paper is the extension of this result to the case of twisted coefficients given by π1Ω|X|−modules A, with π1Ω|X| = H2X.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 121 , Issue 2 , March 1997 , pp. 229 - 245
Copyright
© Cambridge Philosophical Society 1997

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