Finite rigid sets of the non-separating curve complex

TL;DR

This paper proves that for surfaces of genus at least three, the non-separating curve complex can be built up from an increasing sequence of finite rigid subsets, aiding understanding of its structure.

Contribution

It introduces the first construction of an exhaustion by finite rigid sets for the non-separating curve complex of high-genus surfaces.

Findings

Existence of finite rigid set exhaustions for genus ≥ 3 surfaces

Provides a new tool for studying the automorphisms of the non-separating curve complex

Advances understanding of the combinatorial structure of the complex

Abstract

We prove that the non-separating curve complex of every surface of finite type and genus at least three admits an exhaustion by finite rigid sets.