Infinite-type surfaces and their mapping class groups
Introductory Workshop: Topological and Geometric Structures in Low Dimensions & Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups January 26, 2026 - January 30, 2026
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
These talks provide an introduction to mapping class groups of infinite-type surfaces. In the first talk, we survey basic examples of infinite-type surfaces and then turn to general features of their mapping class groups, emphasizing the interplay between the topology of the mapping class group and its algebraic structure.
The second talk focuses on geometric aspects. We first present the general framework of coarsely bounded generation and the resulting large-scale geometry of CB-generated groups, and then illustrate this framework through concrete examples arising from big mapping class groups.