Conjugacy geodesics and growth in dihedral Artin groups
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929728088178688 |
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| author | Ciobanu, Laura Crowe, Gemma |
| author_facet | Ciobanu, Laura Crowe, Gemma |
| contents | In this paper we describe conjugacy geodesic representatives in any dihedral Artin group $G(m)$, $m\geq 3$, which we then use to calculate asymptotics for the conjugacy growth of $G(m)$, and show that the conjugacy growth series of $G(m)$ with respect to the `free product' generating set $\{x, y\}$ is transcendental. We prove two additional properties of $G(m)$ that connect to conjugacy, namely that the permutation conjugator length function is constant, and that the falsification by fellow traveler property (FFTP) holds with respect to $\{x, y\}$. These imply that the language of all conjugacy geodesics in $G(m)$ with respect to $\{x, y\}$ is regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17312 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conjugacy geodesics and growth in dihedral Artin groups Ciobanu, Laura Crowe, Gemma Group Theory 20E45, 20F36, 05E16 In this paper we describe conjugacy geodesic representatives in any dihedral Artin group $G(m)$, $m\geq 3$, which we then use to calculate asymptotics for the conjugacy growth of $G(m)$, and show that the conjugacy growth series of $G(m)$ with respect to the `free product' generating set $\{x, y\}$ is transcendental. We prove two additional properties of $G(m)$ that connect to conjugacy, namely that the permutation conjugator length function is constant, and that the falsification by fellow traveler property (FFTP) holds with respect to $\{x, y\}$. These imply that the language of all conjugacy geodesics in $G(m)$ with respect to $\{x, y\}$ is regular. |
| title | Conjugacy geodesics and growth in dihedral Artin groups |
| topic | Group Theory 20E45, 20F36, 05E16 |
| url | https://arxiv.org/abs/2404.17312 |