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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2403.17964 |
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| _version_ | 1866910790791987200 |
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| author | Kharlampovich, Olga Vdovina, Alina |
| author_facet | Kharlampovich, Olga Vdovina, Alina |
| contents | We answer the question asked by Louder, McReynolds and Patel, and prove the following statement. Let L be a RAAG, H a word quasiconvex subgroup of L, then there is a finite dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate H in L. This implies the same statement for a virtually special group L and, in particular, a fundamental groups of a hyperbolic 3-manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantifying separability in RAAGs via representations Kharlampovich, Olga Vdovina, Alina Group Theory Geometric Topology 20E26, 20C99 We answer the question asked by Louder, McReynolds and Patel, and prove the following statement. Let L be a RAAG, H a word quasiconvex subgroup of L, then there is a finite dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate H in L. This implies the same statement for a virtually special group L and, in particular, a fundamental groups of a hyperbolic 3-manifold. |
| title | Quantifying separability in RAAGs via representations |
| topic | Group Theory Geometric Topology 20E26, 20C99 |
| url | https://arxiv.org/abs/2403.17964 |