Cochain algebras of mapping spaces and finite group actions

Frederic Patras; Jean-Claude Thomas

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arXiv · math/0110213

Cochain algebras of mapping spaces and finite group actions

Frederic Patras·Jean-Claude Thomas

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Abstract

The purpose of the present article is threefold. First of all, we rebuild the whole theory of cosimplicial models of mapping spaces by using systematically Kan adjunction techniques. Secondly, given two topological spaces X and Y, we construct a cochain algebra which is quasi-isomorphic (as an algebra) to the singular cochain algebra of the corresponding mapping space from X to Y. Here, X has to be homotopy equivalent to the geometric realization a finite simplicial set and of dimension less or equal to the connectivity of Y. At last, we apply these results to the study of finite group actions on mapping spaces that are induced by an action on the source.

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BibTeX RIS

Frederic Patras, Jean-Claude Thomas. 2001-10-19. Cochain algebras of mapping spaces and finite group actions. https://arxiv.org/abs/math/0110213

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