Distortion elements in group actions on surfaces

DOI10.1215/S0012-7094-06-13132-0zbMath1088.37009arXivmath/0404532OpenAlexW1973694639MaRDI QIDQ817952

John Franks, Michael Handel

Publication date: 23 March 2006

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0404532

zbMATH Keywords

property Tdistorsiongroup actions on surfacesmeasure-preserving homeomorphism

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) Measurable group actions (22F10)

Related Items (29)

Some ergodic and rigidity properties of discrete Heisenberg group actions ⋮ Distortion in the group of circle homeomorphisms ⋮ Groups of PL homeomorphisms of cubes ⋮ Distortion elements for surface homeomorphisms ⋮ Conjugacy class of homeomorphisms and distortion elements in groups of homeomorphisms ⋮ C¹ actions on manifolds by lattices in Lie groups ⋮ Commuting symplectomorphisms on a surface and the flux homomorphism ⋮ RAAGs in Ham ⋮ Entropy zero area preserving diffeomorphisms of \(S^{2}\) ⋮ Lattice subgroups acting on manifolds ⋮ Existence of orbits with non-zero torsion for certain types of surface diffeomorphisms ⋮ Strong distortion in transformation groups ⋮ Distortion and Tits alternative in smooth mapping class groups ⋮ Maximal pseudometrics and distortion of circle diffeomorphisms ⋮ Actions of solvable Baumslag-Solitar groups on surfaces with (pseudo)-Anosov elements ⋮ Dynamics of affine interval transformations of Higman-Thompson groups \(V_{r, m}\) ⋮ Periodic orbits of Hamiltonian homeomorphisms of surfaces ⋮ Distortion in transformation groups (with an appendix by Yves de Cornulier) ⋮ Large-scale geometry of homeomorphism groups ⋮ Continuity of discrete homomorphisms of diffeomorphism groups ⋮ Global fixed points for centralizers and Morita's theorem ⋮ (Un)distorted diffeomorphisms in different regularities ⋮ Smooth gluing of group actions and applications ⋮ Distortion in groups of affine interval exchange transformations ⋮ Divergence, undistortion and Hölder continuous cocycle superrigidity for full shifts ⋮ Zimmer's conjecture for actions of \(\mathrm{SL}(m,\mathbb{Z})\) ⋮ Zimmer's conjecture: subexponential growth, measure rigidity, and strong property (T) ⋮ Invariant measures and measurable projective factors for actions of higher-rank lattices on manifolds ⋮ Fixed points for nilpotent actions on the plane and the Cartwright-Littlewood theorem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Translation lengths in \(\text{Out}(F_n)\).
• Rational subgroups of biautomatic groups
• A generalization of the Reeb stability theorem
• Real-analytic actions of lattices
• Bounded cohomology of lattices in higher rank Lie groups
• Superrigidity and mapping class groups
• A fixed-point theorem for planar homeomorphisms
• Growth of maps, distortion in groups and symplectic geometry
• Periodic points of Hamiltonian surface diffeomorphisms
• Area preserving group actions on surfaces
• Rank-1 phenomena for mapping class groups
• Connection of the dual space of a group with the structure of its closed subgroups
• Shorter Notes: Invariance of Complementary Domains of a Fixed Point Set
• Recurrence and fixed points of surface homeomorphisms
• [https://portal.mardi4nfdi.de/wiki/Publication:4288848 Sur les groupes engendr�s par des diff�omorphismes proches de l'identit�]
• Rotation Vectors and Fixed Points of Area Preserving Surface Diffeomorphisms
• The word and Riemannian metrics on lattices of semisimple groups

This page was built for publication: Distortion elements in group actions on surfaces