Distance of Edges in the Curve Complex of a Surface

摘要

Let S be a closed orientable surface of genus g ≥ 2,and C(S)the curve complex of S.In the paper,we introduce the concepts of 2-path between edges in C(S),which can be regarded as an analogue to the edge path between vertices in C(S).We show that C(S)is 2P-connected,and the 2-diameter of C(S)is infinite.