Hyperbolicity of the ray graph and quasimorphism on a big modular group

DOI10.2140/GT.2016.20.491zbMath1362.37086arXiv1409.6566OpenAlexW2962939917MaRDI QIDQ258898

Juliette Bavard

Publication date: 10 March 2016

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

Full work available at URL: https://arxiv.org/abs/1409.6566

zbMATH Keywords

Cantor setsmapping class groupssurface homeomorphismsquasimorphismsGromov-hyperbolic spaceray graph

Mathematics Subject Classification ID

Geometric group theory (20F65) Group actions on manifolds and cell complexes in low dimensions (57M60) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30)

Related Items (29)

BIG MAPPING CLASS GROUPS WITH HYPERBOLIC ACTIONS: CLASSIFICATION AND APPLICATIONS ⋮ On the geometry of graphs associated to infinite-type surfaces ⋮ Automorphisms of the loop and arc graph of an infinite-type surface ⋮ Graphs of curves for surfaces with finite-invariance index \(1\) ⋮ The Gromov boundary of the ray graph ⋮ Rotation sets and actions on curves ⋮ Ideally, all infinite‐type surfaces can be triangulated ⋮ Stable commutator length on big mapping class groups ⋮ Two simultaneous actions of big mapping class groups ⋮ Laminations and \(2\)-filling rays on infinite type surfaces ⋮ The grand arc graph ⋮ End‐periodic homeomorphisms and volumes of mapping tori ⋮ Arc and curve graphs for infinite-type surfaces ⋮ Hyperbolic limits of cantor set complements in the sphere ⋮ Large-scale geometry of big mapping class groups ⋮ Sausages ⋮ Flip graphs for infinite type surfaces ⋮ Loxodromic elements in big mapping class groups via the Hooper-Thurston-Veech construction ⋮ Graphs of curves on infinite-type surfaces with mapping class group actions ⋮ Algebraic and topological properties of big mapping class groups ⋮ Distortion and Tits alternative in smooth mapping class groups ⋮ Quasi-morphisms on surface diffeomorphism groups ⋮ Three perfect mapping class groups ⋮ Uniform hyperbolicity of the graphs of nonseparating curves via bicorn curves ⋮ Two remarks about multicurve graphs on infinite-type surfaces ⋮ Big Mapping Class Groups: An Overview ⋮ Big mapping class groups and rigidity of the simple circle ⋮ WWPD elements of big mapping class groups ⋮ Homeomorphic subsurfaces and the omnipresent arcs

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