Year: 2026
Type: preprint
Abstract: We disprove the classical version of the Borsuk-Ulam-flavored conjecture, due to Baum-D{ą}browski-Hajac, that free actions $X\times \mathbb{G}\to X$ on non-empty compact Hausdorff spaces by non-trivial compact groups admit no equivariant maps $X*\mathbb{G}\to X$. Specifically, among non-trivial compact abelian $\mathbb{G}$, the conjecture fails precisely when $\mathbb{G}$ is torsion-free profinite.
Source: arXiv (Cornell University)
Institution: University at Buffalo, State University of New York
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221041066