Geodesic
Graphs of curves and arcs quasi-isometric to big mapping class groups
Anschel Schaffer-Cohen1 orcid
1Universidad Nacional Autónoma de México, Morelia, Mexico
Groups, geometry, and dynamics, Tome 18 (2024) no. 2, pp. 705-735

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DOI

Following the works of Rosendal and Mann and Rafi, we try to answer the following question: when is the mapping class group of an infinite-type surface quasi-isometric to a graph whose vertices are curves on that surface? With the assumption of tameness as defined by Mann and Rafi, we describe a necessary and sufficient condition, called translatability, for a geometrically non-trivial big mapping class group to admit such a quasi-isometry. In addition, we show that the mapping class group of the plane minus a Cantor set is quasi-isometric to the loop graph defined by Bavard, which we believe represents the first known example of a hyperbolic mapping class group that is not virtually free.
DOI : 10.4171/ggd/751
Classification : 20F65, 51F30, 57K20
Mots-clés : big mapping class groups, coarse geometry, curve graphs, quasi-isometry

Anschel Schaffer-Cohen  1

1 Universidad Nacional Autónoma de México, Morelia, Mexico 
Anschel Schaffer-Cohen. Graphs of curves and arcs quasi-isometric to big mapping class groups. Groups, geometry, and dynamics, Tome 18 (2024) no. 2, pp. 705-735. doi: 10.4171/ggd/751
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     number = {2},
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