Abelian Subgroups of the Torelli Group
Abelian Subgroups of the Torelli Group
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托雷利群的阿贝尔子群
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
William R. Vautaw
中科院分区：
文献类型：
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作者：
William R. Vautaw
设S是亏格g > 2的闭定向曲面，T表示它的Torelli群.首先，给定一个集合E的同伦非平凡的，成对不相交，成对非同位素的简单封闭曲线的S，我们精确地确定当一个multitwist在E上是一个元素的T通过定义一个等价关系，然后应用图论。其次，证明了T的任意阿贝尔子群的秩≤ 2g - 3。
Let S be a closed oriented surface of genus g > 2, and let T denote its Torelli group. First, given a set E of homotopically nontrivial, pairwise disjoint, pairwise nonisotopic simple closed curves on S, we determine precisely when a multitwist on E is an element of T by defining an equivalence relation on E and then applying graph theory. Second, we prove that an arbitrary Abelian subgroup of T has rank ≤ 2g - 3.