A free Z-action by isometries on a compact metric space which is not embeddable into a cubical shift
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909798202605568 |
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| author | Dranishnikov, Alexander Levin, Michael |
| author_facet | Dranishnikov, Alexander Levin, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14628 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A free Z-action by isometries on a compact metric space which is not embeddable into a cubical shift Dranishnikov, Alexander Levin, Michael Dynamical Systems Algebraic Topology Geometric Topology 37B02 (55P60, 55P91) 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. |
| title | A free Z-action by isometries on a compact metric space which is not embeddable into a cubical shift |
| topic | Dynamical Systems Algebraic Topology Geometric Topology 37B02 (55P60, 55P91) |
| url | https://arxiv.org/abs/2508.14628 |