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

By C. Costoya, Antonio Viruel. 2011

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We prove that every finite group G can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces X. To construct those spaces we introduce a new technique which leads, for example, to the existence of infinitely many inflexible manifolds. Further applications to representation theory will appear in a separate paper.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9647456f34060c9539f9de6b7f441f4c2c26507c