Conditions on the monodromy for a surface group extension to be CAT(0)
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- by Kejia Zhu
- Proc. Amer. Math. Soc. 151 (2023), 4643-4651
- DOI: https://doi.org/10.1090/proc/16518
- Published electronically: July 28, 2023
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Abstract:
In order to determine when surface-by-surface bundles are non-positively curved, Llosa Isenrich and Py [Math. Ann. 380 (2021), pp. 449–485] give a necessary condition: given a surface-by-surface group $G$ with infinite monodromy, if $G$ is CAT(0) then the monodromy representation is injective. We extend this to a more general result: Let $G$ be a group with a normal surface subgroup $R$. Assume $G/R$ satisfies the property that for every infinite normal subgroup $\Lambda$ of $G/R$, there is an infinite finitely generated subgroup $\Lambda _0<\Lambda$ so that the centralizer $C_{G/R}(\Lambda _0)$ is finite. We then prove that if $G$ is CAT(0) with infinite monodromy, then the monodromy representation has a finite kernel. This applies in particular if $G/R$ is acylindrically hyperbolic.References
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Bibliographic Information
- Kejia Zhu
- Affiliation: Department of Mathematics, University of California, Riverside, California 92507
- MR Author ID: 1499581
- Email: kzhumath@gmail.com
- Received by editor(s): July 1, 2022
- Received by editor(s) in revised form: December 21, 2022, December 22, 2022, and March 27, 2023
- Published electronically: July 28, 2023
- Communicated by: Genevieve S. Walsh
- © Copyright 2023 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 151 (2023), 4643-4651
- MSC (2020): Primary 20F65, 51H30, 20A05
- DOI: https://doi.org/10.1090/proc/16518
- MathSciNet review: 4634870