Mapping class groups of infinite graphs

Abstract: The group of topological symmetries of a surface, known as the mapping class group, provides a powerful lens for studying the geometry and topology of surfaces. The outer automorphism groups of a free group, $\operatorname{Out}(F_n​)$, can be thought of as a graph-theoretic analog of the mapping class group. Although results do not translate directly between the surface and graph settings, their structural parallels inspire questions and techniques between these areas. Over the past decade, there has been a growing interest in studying big mapping class groups, namely those of infinite-type surfaces. In this talk, I will discuss recent progress on the analog of $\operatorname{Out}(F_n​)$ for infinite graphs, including a rigidity theorem, results about the algebraic properties of their asymptotically rigid subgroups, and recent work on actions of these groups on hyperbolic spaces, particularly obstructions to general-type actions.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.