We consider the Type 1 and Type 2 noncommutative Borsuk-Ulam conjectures of Baum, D$ą$browski, and Hajac: there are no equivariant morphisms $A \to A \circledast_δH$ or $H \to A \circledast_δH$, respectively, when $H$ is a nontrivial compact quantum group acting freely on a unital $C^*$-algebra $A$. Here $A \circledast_δH$ denotes the equivariant noncommutative join of $A$ and $H$; this join procedure is a modification of the topological join that allows a free action of $H$ on $A$ to produce a free action of $H$ on $A \circledast_δH$. For the classical case $H = \mathcal{C}(G)$, $G$ a compact group, we present a reduction of the Type 1 conjecture and counterexamples to the Type 2 conjecture. We also present some examples and conditions under which the Type 2 conjecture does hold.

15 pages. Version 4 has an expanded commentary in section 3, including the equivalence of a topological conjecture with a certain noncommutative generalization. To appear in Proceedings of the American Mathematical Society