Past (2025)

January 17th (Fri) 2025, 11 am 

KIAS 1423 & Zoom https://kimsh.kr/vz

Inhyeok Choi (KIAS / Cornell)

Free discrete subgroups of Homeo(S) and the fine curve graph.

Recently, Bowden-Hensel-Webb proposed the notion of the fine curve graph for the study of Homeo(S) as an analogue of the curve graph for the mapping class group Mod(S). In the case of Mod(S), the orbit map from a subgroup of Mod(S) to the curve graph may be seriously distorted. In this talk, I will describe an analogous example for Homeo(S) acting on the fine curve graph, namely, a free discrete subgroup of Homeo(S) without global fixed points, whose one free factor is a loxodromic and the other one free factor fixes the basepoint on the fine curve graph. If time allows, I will explain why the (metric) WPD of point-pushing pseudo-Anosov maps help understand this subgroup. This project is in progress.