Type: Article

Edge-preserving maps of curve graphs

Hernández-Hernández, Jesús;

Abstract:

Suppose S1 and S2 are orientable surfaces of finite topological type such that S1 has genus at least 3 and the complexity of S1 is an upper bound of the complexity of S2. Let ?:C(S1)?C(S2) be an edge-preserving map; then S1 is homeomorphic to S2, and in fact ? is induced by a homeomorphism. To prove this, we use several simplicial properties of rigid expansions, which we prove here.