Homeomorphic subsurfaces and the omnipresent arcs
Annales Henri Lebesgue, Volume 4 (2021), pp. 1565-1593.

Metadata

KeywordsInfinite-type surfaces, subsurfaces, arcs, arc graphs, mapping class groups.

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 an interesting action 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.


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