Type: Article

Rigidity of the nonseparating and outer curve graph

Hernández-Hernández, Jesús;

Abstract:

Let S1 and S2be orientable surfaces of finite topological type with empty boundary,both of genus at least 1 andn1,n2?0 punctures. We define the nonseparating andouter curve graphNO(Si): a particular induced subgraph of the curve graph, which hasthe same large-scale geometry. We prove (under certain conditions on the complexityofS1andS2) that if?:NO(S1)?NO(S2)is a superinjective map, then S1 is homeomorphic toS2and?is induced by a homeomorphism.