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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.31538 |
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| _version_ | 1866913174334210048 |
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| author | Caplinger, Noah |
| author_facet | Caplinger, Noah |
| contents | A hyperbolic structure on a group $G$ is a (not necessarily properly discontinuous) cobounded action of $G$ on a Gromov hyperbolic space, considered up to coarsely $G$-equivariant quasi-isometry. We show that for groups $G$ acting geometrically and positively on a horocyclic product $X\bowtie Y$, all hyperbolic structures on $G$ come from the two actions on the factors. The ingredients of the proof include Malcev rigidity and a new ("vertical") boundary of horocyclic products. We also give the first example of a group acting geometrically on a horocyclic product of two mixed millefeuille spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31538 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Horocyclic products have Y-posets of hyperbolic structures Caplinger, Noah Group Theory A hyperbolic structure on a group $G$ is a (not necessarily properly discontinuous) cobounded action of $G$ on a Gromov hyperbolic space, considered up to coarsely $G$-equivariant quasi-isometry. We show that for groups $G$ acting geometrically and positively on a horocyclic product $X\bowtie Y$, all hyperbolic structures on $G$ come from the two actions on the factors. The ingredients of the proof include Malcev rigidity and a new ("vertical") boundary of horocyclic products. We also give the first example of a group acting geometrically on a horocyclic product of two mixed millefeuille spaces. |
| title | Horocyclic products have Y-posets of hyperbolic structures |
| topic | Group Theory |
| url | https://arxiv.org/abs/2605.31538 |