Edge-preserving maps of curve graphs

Abstract

Suppose $S_1$ and $S_2$ are orientable surfaces of finite topological type such that $S_1$ has genus at least $3$ and the complexity of $S_1$ is an upper bound of the complexity of $S_2$. Let $\phi :\mathcal{C}(S_1)\to \mathcal{C}(S_2)$ be an edge-preserving map; then $S_1$ is homeomorphic to $S_2$, and in fact $\phi$ is induced by a homeomorphism. To prove this, we use several simplicial properties of rigid expansions, which we prove here.

23 pages, 22 figures

Cited by in corpus (2)

• Normal subgroups of mapping class groups and the metaconjecture of Ivanov
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