Cochain algebras of mapping spaces and finite group actions

Details Cochain algebras of mapping spaces and finite group actions Cochain algebras of mapping spaces and finite group actions

2001-10-19

arxiv.org/abs/math/0110213v1

Topology and its Applications, vol. 128, Issues 2-3, (2003), 189-207.

Mathematics

Algebraic Topology

25 pages

Scientific paper

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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