2021/08/15 by Kamlesh Parwani, Parwani, Kamlesh
Biochemistry, Genetics and Molecular Biology · Mathematics · #20F65 (Secondary) #37C05 (Primary) #37E10 #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Protein Tyrosine Phosphatases #math.DS #math.GT #msc:20F65 #msc:37C05 #msc:37E10
paper · pdf · doi:10.48550/arxiv.2108.06814
12 pages. Corrected typos. Incorporated referee comments. Paper has been accepted. arXiv admin note: text overlap with arXiv:0803.4281
openalex publication_date 2021/08/15 · arxiv created 2021/09/28 · arxiv updated 2021/09/29 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Let Σg be a closed, connected, and oriented surface of genus g ≥ 24 and let Γ be a finite index subgroup of the mapping class group Mod(Σg) that contains the Torelli group I(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 n ≥ 8, 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 n ≥ 8, that contains the Torelli group Tn, then any orientation preserving C1 action of Γ on the circle cannot be faithful. In fact, when n ≥ 10, any orientation preserving C1 action of a finite index subgroup of Aut(Fn) or Out(Fn) on the circle cannot be faithful.