Isomorphisms between curve graphs of infinite-type surfaces are geometric

Abstract

Let $\varphi :\mathcal{C}(S)\to \mathcal{C}(S^{\prime })$ be a simplicial isomorphism between the curve graphs of two infinite-type surfaces. In this paper we show that in this situation $S$ and $S^{\prime }$ are homeomorphic and $\varphi$ is induced by a homeomorphism $h:S\to S^{\prime }$.

12 pages, 5 figures