Families of $A_\infty$ algebras and homotopy group actions

Details Families of $A_\infty$ algebras and homotopy group actions Families of $A_\infty$ algebras and homotopy group actions

2009-05-29

arxiv.org/abs/0905.4768v1

Mathematics

Rings and Algebras

23 pages, 4 figures

Scientific paper

We define homotopy group actions in terms of families of $A_\infty$ algebras indexed by a manifold M. We give explicit formulae for the $A_\infty$ morphism induced by a path on the manifold and for the $A_\infty$ 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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