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

2022/03/07 by José M. Moreno-Fernández, Moreno-Fernández, José M., Felix Wierstra +1
Mathematics · #55P62 #55P91 #55U10 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2203.03200

openalex publication_date 2022/03/07 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

We develop the basic theory of Maurer-Cartan simplicial sets associated to (shifted complete) L_∞ 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_∞ 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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