Splittings and poly-freeness of triangle Artin groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917893238685696 |
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| author | Wu, Xiaolei Ye, Shengkui |
| author_facet | Wu, Xiaolei Ye, Shengkui |
| contents | We prove that the triangle Artin group $\mathrm{Art}_{23M}$ splits as a graph of free groups if and only if $M$ is greater than $5$ and even. This answers two questions of Jankiewicz \cite[Question 2.2, Question 2.3]{Jan21} in the negative. Combined with the results of Squier and Jankiewicz, this completely determines when a triangle Artin group splits as a graph of free groups. Furthermore, we prove that the triangle Artin groups are virtually poly-free when the labels are not of the form $(2,3, 2k+1)$ with $k\geq 3$. This partially answers a question of Bestvina \cite{Be99}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08681 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Splittings and poly-freeness of triangle Artin groups Wu, Xiaolei Ye, Shengkui Group Theory Geometric Topology We prove that the triangle Artin group $\mathrm{Art}_{23M}$ splits as a graph of free groups if and only if $M$ is greater than $5$ and even. This answers two questions of Jankiewicz \cite[Question 2.2, Question 2.3]{Jan21} in the negative. Combined with the results of Squier and Jankiewicz, this completely determines when a triangle Artin group splits as a graph of free groups. Furthermore, we prove that the triangle Artin groups are virtually poly-free when the labels are not of the form $(2,3, 2k+1)$ with $k\geq 3$. This partially answers a question of Bestvina \cite{Be99}. |
| title | Splittings and poly-freeness of triangle Artin groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2312.08681 |