Correspondences On Riemann Surfaces: (Non-Uniform) Hyperbolicity and Graph Attractors
发布时间：2026年02月12日
浏览次数：19
发布者: Xiaoni Tan
主讲人： Kevin Pilgrim (Indiana University, US)
活动时间： 从 2026-02-20 09:00 到 10:00
场地： Online
(Joint with L. Bartholdi and D. Dudko)
Abstract:
We consider certain correspondences on a Riemann surface, and show that they admit a weak form of hyperbolicity: sufficiently long loops get shorter under lifting at a fixed point and closing. In terms of their algebraic encoding by bisets, this translates to contraction of fundamental group elements along sequences arising from iterated lifting.
As an application, we show that apart from the usual Latt\`es counterexamples, for any rational map on $P^1$ with $4$ post-critical points, there is a finite invariant collection of isotopy classes of curves into which every curve is attracted under iterated lifting.
Zoom Meeting ID: 181 155 584
