Homeomorphic subsurfaces and omnipresent arcs

In this talk I will discuss infinite-type surfaces (e.g. surfaces of infinite genus). I will show how infinite-type surfaces can be seen as subsurfaces of themselves in a nontrivial way, how to use this fact to select a class of arcs on a surface and to construct a graph with an interesting action by the group of symmetries of the surface (the so-called mapping class group). Joint work with Tyrone Ghaswala and Alan McLeay.