Factoring in the hyperelliptic Torelli group
Factoring in the hyperelliptic Torelli group
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考虑超椭圆 Torelli 群
DOI：
10.1017/s0305004115000286
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发表时间：
2015
影响因子：
0.8
通讯作者：
BRENDLE T
中科院分区：
文献类型：
--
作者：
BRENDLE T
超椭圆Torelli群是映射类群的子群，它由作用于曲面的同调上的平凡元素组成，并与某一固定的超椭圆对合交换。Putman和作者证明了这个群是由超椭圆对合定的分离曲线的Dehn扭曲生成的。在这篇文章中，我们介绍了一种将超椭圆Torelli群的一大类元素分解成Dehn扭曲的算法，并将我们的方法应用于几种基本类型的元素。作为一个结果，我们回答了丹尼斯·约翰逊的一个老问题。
The hyperelliptic Torelli group is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface and that also commute with some fixed hyperelliptic involution. Putman and the authors proved that this group is generated by Dehn twists about separating curves fixed by the hyperelliptic involution. In this paper, we introduce an algorithmic approach to factoring a wide class of elements of the hyperelliptic Torelli group into such Dehn twists, and apply our methods to several basic types of elements. As one consequence, we answer an old question of Dennis Johnson.