Rigidity of mapping class group actions on \(S^1\)

DOI10.2140/gt.2020.24.1211zbMath1454.57014arXiv1808.02979OpenAlexW3091705035MaRDI QIDQ2004524

Kathryn Mann, Maxime Wolff

Publication date: 7 October 2020

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.02979

zbMATH Keywords

rigidityEuler classmapping class groupsurface groupGromov boundaryhomeomorphisms of the circle

Mathematics Subject Classification ID

Topological methods in group theory (57M07) Group actions on manifolds and cell complexes in low dimensions (57M60) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Related Items (9)

Normal generators for mapping class groups are abundant ⋮ \(C^1\) actions on the circle of finite index subgroups of \(\mathrm{Mod}(\Sigma_g)\), \(\mathrm{Aut}(F_n)\), and \(\mathrm{Out}(F_n)\) ⋮ Viterbo conjecture for Zoll symmetric spaces ⋮ Small \(C^1\) actions of semidirect products on compact manifolds ⋮ Groups acting at infinity ⋮ Circularly ordering direct products and the obstruction to left-orderability ⋮ The action spectrum and \(C^0\) symplectic topology ⋮ Barcodes and area-preserving homeomorphisms ⋮ Big mapping class groups and rigidity of the simple circle

Cites Work

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• Basic partitions and combinations of group actions on the circle: A new approach to a theorem of Kathryn Mann
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• Some remarks on foliated \(S^ 1\) bundles
• A characterization of Fuchsian actions by topological rigidity
• Unsmoothable group actions on compact one-manifolds
• Abelian quotients of the Teichmüller modular group
• On the existence of a connection with curvature zero
• Free products and the algebraic structure of diffeomorphism groups
• Breadth in Contemporary Topology
• Dynamical forcing of circular groups

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