Penn Arts & Sciences Logo

"Graphs of curves and arcs quasi-isometric to big mapping class groups"

Geometry-Topology Seminar

Thursday, October 1, 2020 - 4:30pm

Anschel Schaffer-Cohen

UPenn

Location

University of Pennsylvania

via Zoom

The Zoom link is: https://upenn.zoom.us/j/91890239234 This same Zoom link will apply for future talks as well. It is set to open at 4 PM so that speakers can come on early and check out their technology setups. The talks will begin at 4:30 PM. We will also stay afterwards, say from 5:30 - 6 PM to chat with one another, as an online substitute for going out to dinner with our speakers. We encourage everyone to have a nice bottle of wine at hand for that social half hour. For further information about the seminar, please contact Mona Merling (mmerling@math.upenn.edu), Davi Maximo (dmaxim@math.upenn.edu) or Herman Gluck (gluck@math.upenn.edu).

When is a big mapping class group quasi-isometric to a graph whose vertices are curves or arcs on the underlying surface? I will describe a classification of those surfaces whose mapping class groups admit a quasi-isometry to a graph of curves, and provide a specific example of a big mapping class group quasi-isometric to a graph of arcs. As a bonus, I will show that the mapping class group of a plane minus a Cantor set is Gromov-hyperbolic. This talk should be accessible to anyone comfortable with geometric group theory and surface topology.