Graphs of curves on infinite-type surfaces with mapping class group actions
Annales de l'Institut Fourier, Volume 68 (2018) no. 6, pp. 2581-2612.

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.

Nous étudions le cas où le groupe modulaire d’une surface de type infini admet une action avec orbites non bornées sur un graphe connexe dont les sommets sont des courbes fermées simples de S. Nous définissons un invariant topologique pour surfaces de type infini qui détecte dans de nombreux cas s’il y a une telle action. Nous en déduissons que beaucoup de gros groupes modulaires, en tant que groupes topologiques non localement compacts, ont géométrie grossière non banale au sens de Rosendal.

Received:
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Accepted:
Published online:
DOI: 10.5802/aif.3217
Classification: 57S05,  37E30,  20F65,  57M07
Keywords: mapping class groups, surface homeomorphisms, curve graphs, infinite-type surfaces
Durham, Matthew Gentry 1; Fanoni, Federica 2; Vlamis, Nicholas G. 3

1 University of California, Riverside 900 University Ave Riverside, CA 92521 (USA)
2 Universität Heidelberg Im Neuenheimer Feld 205 69120 Heidelberg (Germany)
3 CUNY Queens College Department of Mathematics 65-30 Kissena Blvd Flushing, NY 11367 (USA)
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Durham, Matthew Gentry; Fanoni, Federica; Vlamis, Nicholas G. Graphs of curves on infinite-type surfaces with mapping class group actions. Annales de l'Institut Fourier, Volume 68 (2018) no. 6, pp. 2581-2612. doi : 10.5802/aif.3217. https://aif.centre-mersenne.org/articles/10.5802/aif.3217/

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