\(C^1\) actions on the mapping class groups on the circle

DOI10.2140/agt.2008.8.935zbMath1155.37028arXiv0803.4281OpenAlexW1646228091MaRDI QIDQ945643

Kamlesh Parwani

Publication date: 17 September 2008

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

Full work available at URL: https://arxiv.org/abs/0803.4281

zbMATH Keywords

mapping class groupsKazhdan groupsactions on the circle

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Group actions on manifolds and cell complexes in low dimensions (57M60)

Related Items (10)

\(C^1\) actions on the circle of finite index subgroups of \(\mathrm{Mod}(\Sigma_g)\), \(\mathrm{Aut}(F_n)\), and \(\mathrm{Out}(F_n)\) ⋮ Small \(C^1\) actions of semidirect products on compact manifolds ⋮ A remark on the action of the mapping class group on the unit tangent bundle ⋮ Rigidity of mapping class group actions on \(S^1\) ⋮ A finitely generated, locally indicable group with no faithful action by \(C^1\) diffeomorphisms of the interval ⋮ On the non-realizability of braid groups by diffeomorphisms ⋮ Hyperbolicity as an obstruction to smoothability for one-dimensional actions ⋮ Unsmoothable group actions on compact one-manifolds ⋮ Triviality of some representations of 𝑀𝐶𝐺(𝑆_{𝑔}) in 𝐺𝐿(𝑛,ℂ),𝔻𝕚𝕗𝕗(𝕊²) and ℍ𝕠𝕞𝕖𝕠(𝕋²) ⋮ Diffeomorphism groups of critical regularity

Cites Work

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• A fast method for comparing braids
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• Lattice actions on the circle
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• Groups acting on the circle.
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• Some new rank-1 phenomena for groups of diffeomorphisms of the circle
• The Kazhdan Property of the Mapping Class Group of Closed Surfaces and the First Cohomology Group of Its Cofinite Subgroups
• Arithmetic Groups of Higher ℚ-Rank Cannot Act on 1-Manifolds
• HOMOMORPHISMS FROM AUTOMORPHISM GROUPS OF FREE GROUPS
• Groups of homeomorphisms of one-manifolds III: nilpotent subgroups
• Actions de groupes de Kazhdan sur le cercle
• Dynamical forcing of circular groups

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