Free Semigroups of Large Critical Exponent
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916647732772864 |
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| author | Skenderi, Aleksander |
| author_facet | Skenderi, Aleksander |
| contents | For a convergence group equipped with an expanding coarse-cocycle, we construct finitely generated free subsemigroups, which we call $\textit{Bishop--Jones}$ $\textit{semigroups}$, of critical exponent arbitrarily close to but strictly less than the critical exponent of the ambient group. As an application, we show that for any non-elementary transverse subgroup $Γ$ of a semisimple Lie group $G$, there exist finitely generated free Anosov subsemigroups in the sense of Kassel--Potrie of critical exponent arbitrarily close to but strictly less than that of the ambient transverse group. Furthermore, we show that these semigroups admit $\mathcal{C}$-regular quasi-isometric embeddings into the symmetric space $X$ of $G$, in the sense of Kapovich--Leeb--Porti. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free Semigroups of Large Critical Exponent Skenderi, Aleksander Group Theory Dynamical Systems Geometric Topology For a convergence group equipped with an expanding coarse-cocycle, we construct finitely generated free subsemigroups, which we call $\textit{Bishop--Jones}$ $\textit{semigroups}$, of critical exponent arbitrarily close to but strictly less than the critical exponent of the ambient group. As an application, we show that for any non-elementary transverse subgroup $Γ$ of a semisimple Lie group $G$, there exist finitely generated free Anosov subsemigroups in the sense of Kassel--Potrie of critical exponent arbitrarily close to but strictly less than that of the ambient transverse group. Furthermore, we show that these semigroups admit $\mathcal{C}$-regular quasi-isometric embeddings into the symmetric space $X$ of $G$, in the sense of Kapovich--Leeb--Porti. |
| title | Free Semigroups of Large Critical Exponent |
| topic | Group Theory Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2502.02003 |