Speaker: Tianyi Lou (Université Côte d’Azur)
Time: 14:30-15:30, Sep 24, 2026
Venue: room 1329, Building 1 (Section A), New Campus of USTC Shanghai Institute for Advanced Studies & Tencent Meeting ID: 942 663 0176, password: 202501
Mapping class groups of finite-type surfaces are well understood and exhibit rich dynamics. In contrast, mapping class groups of infinite-type surfaces (big mapping class groups) are less explored and often fall outside standard frameworks. Abbott-Dahmani showed that acylindrically hyperbolic groups (without non-trivial finite normal subgroups) satisfy property $P_{\mathrm{naive}}$. But for an infinite-type surface $S$, $\mathrm{Map}(S)$ is not acylindrically hyperbolic, so that result cannot be applied. Assuming that $S$ contains a nondisplaceable finite-type subsurface, Horbez-Qing-Rafi construct a continuous nonelementary action of $\mathrm{Map}(S)$ on a hyperbolic quasi-tree of curve graphs. We use this action to prove that $\mathrm{Map}(S)$ has $P_{\mathrm{naive}}$ for orientable $S$ and non-orientable $S$: for any finite collection of non-trivial elements $h_1,\dots,h_n$, there exists an infinite-order element $g\neq 1$ such that $\langle g,h_i\rangle \cong \langle g\rangle * \langle h_i\rangle$ for all $i$.
