Cyclic orders and actions of Leary--Minasyan groups on coarse $\mathrm{PD}(n)$ spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909718505586688 |
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| author | Banerjee, Arka Schreve, Kevin |
| author_facet | Banerjee, Arka Schreve, Kevin |
| contents | We show that for $n \geq 3$, there are torsion-free CAT(0) groups with visual boundaries that embed into $S^n$ but which are not virtually the fundamental group of a compact aspherical $n+1$-manifold. The groups are the CAT(0) and not bi-automatic groups constructed previously by Leary and Minasyan. The obstruction comes from analyzing certain cyclic orders on the boundary of the Bass-Serre tree, in the same manner as Kapovich-Kleiner ruled out actions of Baumslag-Solitar groups on coarse $\mathrm{PD}(3)$ spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01075 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclic orders and actions of Leary--Minasyan groups on coarse $\mathrm{PD}(n)$ spaces Banerjee, Arka Schreve, Kevin Group Theory Geometric Topology Metric Geometry We show that for $n \geq 3$, there are torsion-free CAT(0) groups with visual boundaries that embed into $S^n$ but which are not virtually the fundamental group of a compact aspherical $n+1$-manifold. The groups are the CAT(0) and not bi-automatic groups constructed previously by Leary and Minasyan. The obstruction comes from analyzing certain cyclic orders on the boundary of the Bass-Serre tree, in the same manner as Kapovich-Kleiner ruled out actions of Baumslag-Solitar groups on coarse $\mathrm{PD}(3)$ spaces. |
| title | Cyclic orders and actions of Leary--Minasyan groups on coarse $\mathrm{PD}(n)$ spaces |
| topic | Group Theory Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2508.01075 |