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arXiv · 2508.14628

A free Z-action by isometries on a compact metric space which is not embeddable into a cubical shift

Alexander Dranishnikov·Michael Levin
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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.

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Alexander Dranishnikov, Michael Levin. 2025-08-20. A free Z-action by isometries on a compact metric space which is not embeddable into a cubical shift. https://arxiv.org/abs/2508.14628

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