Singular value gap estimates for free products of semigroups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917790730944512 |
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| author | Tsouvalas, Konstantinos Weisman, Theodore |
| author_facet | Tsouvalas, Konstantinos Weisman, Theodore |
| contents | We establish lower estimates for singular value gaps of free products of $1$-divergent semigroups $Γ_1,Γ_2\subset \mathsf{GL}_d(\mathbb{K})$ which are in ping-pong position. As an application, we prove that if $Γ_1$ and $Γ_2$ are quasi-isometrically embedded subgroups in ping pong position, then the group they generate $\langle Γ_1,Γ_2\rangle$ is also quasi-isometrically embedded. In addition, we establish that the class of linear finitely generated groups, admitting a faithful linear representation over $\mathbb{R}$ which is a quasi-isometric embedding, is closed under free products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_20330 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular value gap estimates for free products of semigroups Tsouvalas, Konstantinos Weisman, Theodore Group Theory Geometric Topology We establish lower estimates for singular value gaps of free products of $1$-divergent semigroups $Γ_1,Γ_2\subset \mathsf{GL}_d(\mathbb{K})$ which are in ping-pong position. As an application, we prove that if $Γ_1$ and $Γ_2$ are quasi-isometrically embedded subgroups in ping pong position, then the group they generate $\langle Γ_1,Γ_2\rangle$ is also quasi-isometrically embedded. In addition, we establish that the class of linear finitely generated groups, admitting a faithful linear representation over $\mathbb{R}$ which is a quasi-isometric embedding, is closed under free products. |
| title | Singular value gap estimates for free products of semigroups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2409.20330 |