Edge Preserving Maps of the Curve Graphs in Low Genus

Abstract

Let $R$ be a compact, connected, orientable surface of genus $g$ with $n$ boundary components. Let $\mathcal{C}(R)$ be the curve graph of $R$. We prove that if $g=0,n\ge 5$ or $g=1,n\ge 3$, and $\lambda :\mathcal{C}(R)\to \mathcal{C}(R)$ is an edge preserving map, then $\lambda$ is induced by a homeomorphism of $R$, and this homeomorphism is unique up to isotopy.

25 pages, 14 figures. arXiv admin note: text overlap with arXiv:1708.05290

References in corpus (1)

• Edge-preserving maps of curve graphs

Cited by in corpus (1)

• Graph morphisms and exhaustion of curve graphs of low-genus surfaces