A free Z-action by isometries on a compact metric space which is not embeddable into a cubical shift
Dynamical Systems
2025-09-23 v1 Algebraic Topology
Geometric Topology
Abstract
We construct an example announced in the title. It answers in a strong way a well-known open problem in topological dynamics. In fact our construction is an existence theorem. It is based on a Borsuk-Ulam type theorem whose proof heavily relies on p-adic completions of G-complexes and the equivariant Sullivan conjecture.
Keywords
Cite
@article{arxiv.2508.14628,
title = {A free Z-action by isometries on a compact metric space which is not embeddable into a cubical shift},
author = {Alexander Dranishnikov and Michael Levin},
journal= {arXiv preprint arXiv:2508.14628},
year = {2025}
}