On the homotopy fixed points of Maurer-Cartan spaces with finite group actions

José M. Moreno-Fernández; Felix Wierstra

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arXiv · 2203.03200

On the homotopy fixed points of Maurer-Cartan spaces with finite group actions

José M. Moreno-Fernández·Felix Wierstra

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Abstract

We develop the basic theory of Maurer-Cartan simplicial sets associated to (shifted complete) $L_\infty$ algebras equipped with the action of a finite group. Our main result asserts that the inclusion of the fixed points of this equivariant simplicial set into the homotopy fixed points is a homotopy equivalence of Kan complexes, provided the $L_\infty$ algebra is concentrated in non-negative degrees. As an application, and under certain connectivity assumptions, we provide rational algebraic models of the fixed and homotopy fixed points of mapping spaces equipped with the action of a finite group.

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BibTeX RIS

José M. Moreno-Fernández, Felix Wierstra. 2022-03-07. On the homotopy fixed points of Maurer-Cartan spaces with finite group actions. https://arxiv.org/abs/2203.03200

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