3 problems

Let $X$ be a compact Hausdorff space with a continuous free action of a nontrivial compact Hausdorff group $G$. Let $X*G$ denote the join equipped with the diagonal action of $G$.…

Noncommutative Borsuk–Ulam conjecture. There does not exist a $\mathbb{G}$-equivariant $*$-homomorphism

Let $G=\mathbb{Z}_{p^k}$, and let ${\perp}W^G$ be the complex $G$-representation appearing in the construction above, with $m$ denoting the relevant multiplicity. For the length in…