Homeomorphic subsurfaces and the omnipresent arcs

TL;DR

This paper explores the topology of arcs on surfaces, introduces a new way to characterize infinite-type surfaces via homeomorphic subsurfaces, and constructs mapping class group actions on arc subgraphs.

Contribution

It provides a novel topological characterization of infinite-type surfaces and constructs new group actions on arc subgraphs based on this framework.

Findings

Topological insights into arcs and their complements

A new characterization of infinite-type surfaces

Construction of mapping class group actions on arc subgraphs

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.