Groups acting on horocyclic products
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912721862131712 |
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| author | Caplinger, Noah Levitin, Daniel N. |
| author_facet | Caplinger, Noah Levitin, Daniel N. |
| contents | Horocyclic products are a well-studied class of metric spaces that provide models for various solvable Lie groups, Baumslag-Solitar groups, and Lamplighter groups. Let $G$ act geometrically on a horocyclic product $X \bowtie Y$ of $\CAT(-κ)$ spaces $X,Y$. We show that every such group is either an ascending HNN extension of a finitely-generated virtually nilpotent group, or else is not finitely presented, depending on the connectivity of the visual boundary of $X\bowtie Y$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Groups acting on horocyclic products Caplinger, Noah Levitin, Daniel N. Group Theory Geometric Topology Horocyclic products are a well-studied class of metric spaces that provide models for various solvable Lie groups, Baumslag-Solitar groups, and Lamplighter groups. Let $G$ act geometrically on a horocyclic product $X \bowtie Y$ of $\CAT(-κ)$ spaces $X,Y$. We show that every such group is either an ascending HNN extension of a finitely-generated virtually nilpotent group, or else is not finitely presented, depending on the connectivity of the visual boundary of $X\bowtie Y$. |
| title | Groups acting on horocyclic products |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2511.16809 |