Graphs of curves on infinite-type surfaces with mapping class group actions

Abstract

Graphs of curves on infinite-type surfaces with mapping class group actions

Big mapping class groups and rigidity of the simple circle

“…It is the best understood and most studied example of a so-called 'big' mapping class group; see e.g. [1,10,15].…”

Big mapping class groups: an overview

“…These different phenomena were clarified in subsequent work of Durham, Fanoni and the second author [38]. The motivation of their work was to find actions of big mapping class group not relying on isolated planar ends.…”

“…The following theorem is a reformulated version of [13, Theorem 1] (see also [38,Section 6] for another formulation). In an intuitive way, it encapsulates the idea of taking a limit of a family of uniformly hyperbolic spaces: Theorem 6.5.…”

Matching arc complexes: connectedness and hyperbolicity

“…Our proof of Theorem 1.2 adapts the unicorn path machinery of Hensel-Przytycki-Webb [11], which they used to prove the uniform hyperbolicity of arc graphs (the 1-skeleta of arc complexes). The difficulties we encounter boil down to the fact that a unicorn path between two vertices of MApS, Γq may contain edges that do not belong to MApS, Γq; in order to overcome this problem, we will use the structure of Γ, plus techniques similar in spirit to those of [7,Section 5].…”