| Distance of Edges in the Curve Complex of a Surface |
| Received:April 22, 2011 Revised:September 01, 2011 |
| Key Words:
curve complex distance of vertices 2-path between edges 2-diameter of $C(S)$.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10931005). |
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| Abstract: |
| Let $S$ be a closed orientable surface of genus $g\geq 2$, 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.06.018 |
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