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June 2022 C1 actions on the circle of finite index subgroups of Mod(Σg), Aut(Fn), and Out(Fn)
Kamlesh Parwani
Rocky Mountain J. Math. 52(3): 1021-1029 (June 2022). DOI: 10.1216/rmj.2022.52.1021

Abstract

Let Σg be a closed, connected, and oriented surface of genus g24, and let Γ be a finite index subgroup of the mapping class group Mod(Σg) that contains the Torelli group (Σg). Then any orientation-preserving C1 action of Γ on the circle cannot be faithful.

We also show that if Γ is a finite index subgroup of Aut(Fn), when n8, that contains the subgroup of IA-automorphisms, then any orientation-preserving C1 action of Γ on the circle cannot be faithful.

Similarly, if Γ is a finite index subgroup of Out(Fn), when n8, that contains the Torelli group 𝒯n, then any orientation preserving C1 action of Γ on the circle cannot be faithful.

In fact, when n10, any orientation-preserving C1 action of a finite index subgroup of Aut(Fn) or Out(Fn) on the circle cannot be faithful.

Citation

Download Citation

Kamlesh Parwani. "C1 actions on the circle of finite index subgroups of Mod(Σg), Aut(Fn), and Out(Fn)." Rocky Mountain J. Math. 52 (3) 1021 - 1029, June 2022. https://doi.org/10.1216/rmj.2022.52.1021

Information

Received: 31 August 2021; Revised: 14 September 2021; Accepted: 14 September 2021; Published: June 2022
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.1216/rmj.2022.52.1021

Subjects:
Primary: 37C05 , 37E10
Secondary: 20F65

Keywords: circle diffeomorphisms , group actions , mapping class group

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 3 • June 2022
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