Faithful actions on Differential Graded Algebras determine the isomorphism type of a large class of groups

Abstract

We prove that the isomorphism type of a large class of groups (containing finite groups, countable Artinian groups and mapping class groups of certain surfaces, among others) is determined by the set of differential graded $\mathbb{Q}$-algebras on which these groups act faithfully.

7 pages, no figures

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• Every finite group is the group of self homotopy equivalences of an elliptic space