Splittings and poly-freeness of triangle Artin groups
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- by Xiaolei Wu and Shengkui Ye;
- Trans. Amer. Math. Soc. 378 (2025), 4707-4737
- DOI: https://doi.org/10.1090/tran/9408
- Published electronically: April 4, 2025
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Abstract:
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 [Groups Geom. Dyn. 18 (2024), pp. 91–108; Question 2.2, Question 2.3] 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 [Geom. Topol. 3 (1999), pp. 269–302].References
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Bibliographic Information
- Xiaolei Wu
- Affiliation: Shanghai Center for Mathematical Sciences, Jiangwan Campus, Fudan University, No.2005 Songhu Road, Shanghai 200438, People’s Republic of China
- MR Author ID: 1071753
- ORCID: 0000-0003-2064-4455
- Email: xiaoleiwu@fudan.edu.cn
- Shengkui Ye
- Affiliation: NYU Shanghai, No.567 Yangsi West Rd, Pudong New Area, Shanghai 200124, People’s Republic of China; and NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, People’s Republic of China
- MR Author ID: 834051
- Email: sy55@nyu.edu
- Received by editor(s): January 20, 2024
- Received by editor(s) in revised form: October 28, 2024
- Published electronically: April 4, 2025
- Additional Notes: The first author is currently a member of LMNS and was supported by a starter grant at Fudan University. The second author was supported by NSFC (No. 11971389).
- © Copyright 2025 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 378 (2025), 4707-4737
- MSC (2020): Primary 20F65
- DOI: https://doi.org/10.1090/tran/9408