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Families of A_∞ algebras and homotopy group actions

2009/05/29 by Emma Smith Zbarsky, Zbarsky, Emma Smith
Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AT #math.RA

paper · pdf · doi:10.48550/arxiv.0905.4768

23 pages, 4 figures

arxiv created 2009/05/29 · arxiv updated 2009/12/01

Abstract

We define homotopy group actions in terms of families of A_∞ algebras indexed by a manifold M. We give explicit formulae for the A_∞ morphism induced by a path on the manifold and for the A_∞ homotopy corresponding to a pair of homotopic paths. Finally, we compute examples for finite groups and finitely generated free nonabelian groups and determine that every homotopy group action by a finite group is homotopic to a strict group action.

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