Hyperbolicity as an obstruction to smoothability for one-dimensional actions

DOI10.2140/gt.2019.23.1841zbMath1428.37029arXiv1706.05704OpenAlexW3104048157MaRDI QIDQ2318708

Michele Triestino, Yash Lodha, Christian Bonatti

Publication date: 16 August 2019

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

Full work available at URL: https://arxiv.org/abs/1706.05704

zbMATH Keywords

hyperbolic dynamicsgroup actions on the intervalpiecewise-projective homeomorphisms

Mathematics Subject Classification ID

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) Dynamical systems involving maps of the interval (37E05) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Means on groups, semigroups, etc.; amenable groups (43A07) Obstructions to group actions ((K)-theoretic aspects) (19J35)

Related Items (6)

The BNSR-invariants of the Lodha–Moore groups, and an exotic simple group of type ⋮ Generic algebraic properties in spaces of enumerated groups ⋮ A finitely presented infinite simple group of homeomorphisms of the circle ⋮ Coherent actions by homeomorphisms on the real line or an interval ⋮ Finitely generated infinite simple groups of homeomorphisms of the real line ⋮ Diffeomorphism groups of critical regularity

Cites Work

• A nonamenable finitely presented group of piecewise projective homeomorphisms
• Rigidity of certain solvable actions on the sphere
• \(C^1\)-actions of Baumslag-Solitar groups on \(S^1\)
• Centralizers of \(C^1\)-contractions of the half line
• Nonsmoothable, locally indicable group actions on the interval
• \(C^1\) actions on the mapping class groups on the circle
• A finitely generated, locally indicable group with no faithful action by \(C^1\) diffeomorphisms of the interval
• Groups of piecewise linear homeomorphisms of the real line
• Sur un groupe remarquable de difféomorphismes du cercle. (On a remarkable group of the diffeomorphisms of the circle)
• A generalization of the Reeb stability theorem
• Bounded cohomology of lattices in higher rank Lie groups
• Lattice actions on the circle
• Introductory notes on Richard Thompson's groups
• Classification of exotic circles of \(PL_+(S^1)\)
• Commutators in groups of piecewise projective homeomorphisms
• Groups of fast homeomorphisms of the interval and the ping-pong argument
• Global rigidity of solvable group actions on \(S^1\)
• Exotic circles of \(PL_ + (S^ 1)\)
• Actions of Baumslag-Solitar groups on surfaces
• Unsmoothable group actions on compact one-manifolds
• Rigidity for \(C^1\) actions on the interval arising from hyperbolicity. I: Solvable groups
• On one-dimensional dynamics in intermediary regularity
• Rotation numbers in Thompson-Stein groups and applications
• Some new rank-1 phenomena for groups of diffeomorphisms of the circle
• Regular iteration of real and complex functions
• On Groups of PL-homeomorphisms of the Real Line
• Rigidity of trivial actions of abelian-by-cyclic groups
• Groups of Piecewise Linear Homeomorphisms
• Arithmetic Groups of Higher ℚ-Rank Cannot Act on 1-Manifolds
• Actions de groupes de Kazhdan sur le cercle
• Groups of piecewise projective homeomorphisms
• Dynamical forcing of circular groups

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