On Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866916553925066752 |
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| author | Dey, Subhadip |
| author_facet | Dey, Subhadip |
| contents | We study the antipodal subsets of the full flag manifolds $\mathcal{F}(\mathbb{R}^d)$. As a consequence, for natural numbers $d \ge 2$ such that $d\ne 5$ and $d \not\equiv 0,\pm1 \mod 8$, we show that Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$ are virtually isomorphic to either a free group or the fundamental group of a closed hyperbolic surface. This gives a partial answer to a question asked by Andrés Sambarino. Furthermore, we show restrictions on the hyperbolic spaces admitting uniformly regular quasi-isometric embeddings into the symmetric space $X_d$ of ${\rm SL}(d,\mathbb{R})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_02109 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$ Dey, Subhadip Geometric Topology Group Theory 22E40, 14M15, 20F65 We study the antipodal subsets of the full flag manifolds $\mathcal{F}(\mathbb{R}^d)$. As a consequence, for natural numbers $d \ge 2$ such that $d\ne 5$ and $d \not\equiv 0,\pm1 \mod 8$, we show that Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$ are virtually isomorphic to either a free group or the fundamental group of a closed hyperbolic surface. This gives a partial answer to a question asked by Andrés Sambarino. Furthermore, we show restrictions on the hyperbolic spaces admitting uniformly regular quasi-isometric embeddings into the symmetric space $X_d$ of ${\rm SL}(d,\mathbb{R})$. |
| title | On Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$ |
| topic | Geometric Topology Group Theory 22E40, 14M15, 20F65 |
| url | https://arxiv.org/abs/2208.02109 |