曲面上曲线复形中边的距离

Distance of Edges in the Curve Complex of a Surface

中文关键词:  曲线复形  顶点距离  2-道路  $C(S)$的2-直径.

英文关键词:curve complex  distance of vertices  2-path between edges  2-diameter of $C(S)$.

中文摘要:

      设$S$是一个亏格$g\geq 2$的闭可定向曲面,$C(S)$是$S$上的曲线复形.在本文中,我们介绍了$C(S)$中边的2-道路的定义,它可以看做是$C(S)$中顶点之间边道路的推广.我们证明了$C(S)$是$2P$-连通的,并且它的2-直径是无穷的.

英文摘要:

      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.