On the ideal triangulation graph of a punctured surface
On the ideal triangulation graph of a punctured surface
复制标题
DOI：
10.5802/aif.2725
复制
发表时间：
2009-10
期刊：
影响因子：
--
通讯作者：
Mustafa Korkmaz;A. Papadopoulos
中科院分区：
文献类型：
--
作者：
Mustafa Korkmaz;A. Papadopoulos
研究了有限型穿孔曲面S的理想三角剖分图T(S)。证明了如果S不是至多有三个穿孔的球面，也不是一个有一个穿孔的环面，那么从S的扩张映射类群到T(S)的单纯自同构群的自然映射是同构的。我们还证明了在S的相同条件下，赋其自然单纯度量的图T(S)不是Gromov双曲的。因此，从格罗莫夫双曲性的角度来看，T(S)的情况不同于S.AMS数学学科分类：初级32G15的曲线复合体的情况。次级20F38；30F10。
We study the ideal triangulation graph T (S) of a punctured surface S of finite type. We show that if S is not the sphere with at most three punctures or the torus with one puncture, then the natural map from the extended mapping class group of S into the simplicial automorphism group of T (S) is an isomorphism. We also show that under the same conditions on S, the graph T (S) equipped with its natural simplicial metric is not Gromov hyperbolic. Thus, from the point of view of Gromov hyperbolicity, the situation of T (S) is different from that of the curve complex of S. AMS Mathematics Subject Classification: Primary 32G15. Secondary 20F38 ; 30F10.