2 problems

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

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 $G$.…