Anosov representations of amalgams
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913813199060992 |
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| author | Dey, Subhadip Tsouvalas, Konstantinos |
| author_facet | Dey, Subhadip Tsouvalas, Konstantinos |
| contents | For uniform lattices $Γ$ in rank 1 Lie groups, we construct Anosov representations of virtual doubles of $Γ$ along certain quasiconvex subgroups. We also show that virtual HNN extensions of these lattices over some cyclic subgroups admit Anosov embeddings. In addition, we prove that for any Anosov subgroup $Γ$ of a real semisimple linear Lie group $\mathsf{G}$ and any infinite abelian subgroup $\mathrm{H} $ of $ Γ$, there exists a finite-index subgroup $Γ' $ of $ Γ$ containing $\mathrm{H}$ such that the double $Γ' *_{\mathrm{H}} Γ'$ admits an Anosov representation, thereby confirming a conjecture of [arXiv:2112.05574]. These results yield numerous examples of one-ended hyperbolic groups that do not admit discrete and faithful representations into rank 1 Lie groups but do admit Anosov embeddings into higher-rank Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21802 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anosov representations of amalgams Dey, Subhadip Tsouvalas, Konstantinos Group Theory Dynamical Systems Geometric Topology 22E40, 53C35, 20F65, 14M15 For uniform lattices $Γ$ in rank 1 Lie groups, we construct Anosov representations of virtual doubles of $Γ$ along certain quasiconvex subgroups. We also show that virtual HNN extensions of these lattices over some cyclic subgroups admit Anosov embeddings. In addition, we prove that for any Anosov subgroup $Γ$ of a real semisimple linear Lie group $\mathsf{G}$ and any infinite abelian subgroup $\mathrm{H} $ of $ Γ$, there exists a finite-index subgroup $Γ' $ of $ Γ$ containing $\mathrm{H}$ such that the double $Γ' *_{\mathrm{H}} Γ'$ admits an Anosov representation, thereby confirming a conjecture of [arXiv:2112.05574]. These results yield numerous examples of one-ended hyperbolic groups that do not admit discrete and faithful representations into rank 1 Lie groups but do admit Anosov embeddings into higher-rank Lie groups. |
| title | Anosov representations of amalgams |
| topic | Group Theory Dynamical Systems Geometric Topology 22E40, 53C35, 20F65, 14M15 |
| url | https://arxiv.org/abs/2504.21802 |