Homeomorphic subsurfaces and the omnipresent arcs
arXiv:2003.04750
Abstract
In this article, we are concerned with various aspects of arcs on surfaces. In the first part, we deal with topological aspects of arcs and their complements. We use this understanding, in the second part, to construct interesting actions of the mapping class group on a subgraph of the arc graph. This subgraph naturally emerges from a new characterisation of infinite-type surfaces in terms of homeomorphic subsurfaces.
To correct an error in the previous version, Sections 6 and 7 have been combined and rewritten into what is now Section 6. Other minor changes have also been made. To appear in Annales Henri Lebesgue