2000 character limit reached
Coarsely bounded generating sets for mapping class groups of infinite-type surfaces
Published 4 Dec 2023 in math.GT | (2312.02361v2)
Abstract: Mann and Rafi's seminal work initiated the study of the coarse geometry of big mapping class groups. Specifically, they construct coarsely bounded (CB) generating sets for mapping class groups of a large class of infinite-type surfaces. In this expository note, we illustrate examples of surfaces whose mapping class groups admit such generating sets, as well as those that do not, with the goal of exploring the context of Mann--Rafi's hypotheses.
- Big mapping class groups: an overview. In In the tradition of Thurston—geometry and topology, pages 459–496. Springer, Cham, [2020] ©2020.
- Danny Calegari. Mapping class groups and dynamics, 2009. https://lamington.wordpress.com/2009/06/22/big-mapping-class-groups-and-dynamics/.
- Thomas Hill. Large-scale geometry of pure mapping class groups of infinite-type surfaces, 2023.
- Two results on end spaces of infinite type surfaces. arXiv preprint arXiv:2201.07690, 2022. To appear in Michigan Math J.
- Large-scale geometry of big mapping class groups. Geom. Topol., 27(6):2237–2296, 2023.
- Ian Richards. On the classification of noncompact surfaces. Trans. Amer. Math. Soc., 106:259–269, 1963.
- On the large scale geometry of big mapping class groups of surfaces with a unique maximal end. arXiv preprint arXiv:2309.05820, 2023.
- Christian Rosendal. Coarse geometry of topological groups, volume 223 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 2022.
- Nicholas G Vlamis. Notes on the topology of mapping class groups. preprint, 2019.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.