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

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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.

SEEK ID: https://publications.h-its.org/publications/931

DOI: 10.5802/aif.3217

Research Groups: Groups and Geometry

Publication type: Book

Journal: Annales de l'Institut Fourier

Citation: Annales de l'Institut Fourier 68(6):2581-2612

Date Published: 2018

Registered Mode: imported from a bibtex file

Authors: Matthew Gentry Durham, Federica Fanoni, Nicholas G. Vlamis

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Lukas Sauer

Citation

Durham, M. G., Fanoni, F., & Vlamis, N. G. (2018). Graphs of curves on infinite-type surfaces with mapping class group actions. In Annales de l'Institut Fourier (Vol. 68, Issue 6, pp. 2581–2612). Cellule MathDoc/CEDRAM. https://doi.org/10.5802/aif.3217

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Created: 13th Jan 2020 at 13:41

Last updated: 5th Mar 2024 at 21:24

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

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