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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.16360 |
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| _version_ | 1866910381458325504 |
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| author | Fernós, Talia |
| author_facet | Fernós, Talia |
| contents | We revisit the topic of probability measures on CAT(0) cube complexes and prove that an amenable group acting on a CAT(0) cube complex, regardless of dimension, necessarily preserves an interval in the Roller compactification. In the finite dimensional case, we prove that there must be an orbit of cardinality $2^N$, where $N$ is bounded by the dimension. This is a slight extension of the author's previous Tits' Alternative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16360 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Le Conte de la Mesure sur les Complexes Cubiques CAT(0) Fernós, Talia Group Theory Primary 20F65, 20E05, 60B05, Secondary 05C12, 05E18, 06A07, 20F29 We revisit the topic of probability measures on CAT(0) cube complexes and prove that an amenable group acting on a CAT(0) cube complex, regardless of dimension, necessarily preserves an interval in the Roller compactification. In the finite dimensional case, we prove that there must be an orbit of cardinality $2^N$, where $N$ is bounded by the dimension. This is a slight extension of the author's previous Tits' Alternative. |
| title | Le Conte de la Mesure sur les Complexes Cubiques CAT(0) |
| topic | Group Theory Primary 20F65, 20E05, 60B05, Secondary 05C12, 05E18, 06A07, 20F29 |
| url | https://arxiv.org/abs/2403.16360 |