THE BORSUK-ULAM THEOREM FOR LOCALLY TRIVIAL COMPACT G-SPACES

The Borsuk-Ulam-type conjecture of Baum, Dąbrowski, and Hajac states that, given a free action of a non-trivial compact Hausdorff group G on a compact Hausdorff space X, there is no continuous G-equivariant map from the join X*G to X. The goal of this talk is to explain a proof of this conjecture for locally trivial compact G-spaces. This case boils down to the claim that there is no G-equivariant continuous map from the (n+1) join power of G to the n join power of G, which is a slight strengthening of an unpublished result of Bestvina and Edwards. (Based on joint work with Alexandru Chirvasitu and Ludwik Dąbrowski.)