Graphs of curves on infinite-type surfaces with mapping class group actions

Abstract

We study when the mapping class group of an infinite-type surface $S$ admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on $S$. We introduce a topological invariant for infinite-type surfaces that determines in many cases whether there is such an action. This allows us to conclude that, as non-locally compact topological groups, many big mapping class groups have nontrivial coarse geometry in the sense of Rosendal.

25 pages, 5 figures. v3: Final version, incorporates referee's comments, to appear at Annales de l'Institut Fourier

Cited by in corpus (8)

• Big mapping class groups: an overview
• Large scale geometry of big mapping class groups
• The first integral cohomology of pure mapping class groups
• Big mapping class groups and rigidity of the simple circle
• Big mapping class groups with hyperbolic actions: classification and applications
• Loxodromic elements in big mapping class groups via the Hooper-Thurston-Veech construction
• Coarse Geometry of Pure Mapping Class Groups of Infinite Graphs
• Matching arc complexes: connectedness and hyperbolicity