turkmath.org

A homotopy action of a group G on a topological space X is a group homomorphism from G to the group of homotopy classes of self-homotopy equivalences of X. George Cooke described an obstruction theory for realizing a homotopy action of a finite group G on a space X by strict action. However, the resulting G-space is only determined up to a homotopy equivalence which is a G-map (Borel equivalence), and in this sense every G-space is equivalent to a free one. So the more delicate aspects of equivariant topology are not visible in this way. A more informative approach to equivariant homotopy theory, due to Bredon, studies G-spaces X up to G-homotopy equivalence, that is, G-maps having G-homotopy inverses. The purpose of this talk is to define a notion of homotopy action of a finite group in Bredon equivariant homotopy theory, and describe an associated inductive procedure for realizing such an action by a strict one. (This is a joint work with Prof. David Blanc)