Floer Homology and Fractional Dehn Twists
Floer Homology and Fractional Dehn Twists
复制标题
DOI：
10.1016/j.aim.2017.11.008
复制
发表时间：
2015-01
期刊：
影响因子：
--
通讯作者：
M. Hedden;Thomas E. Mark
中科院分区：
文献类型：
--
作者：
M. Hedden;Thomas E. Mark
我们建立了Heegaard Floer同调和表面自同构的分数Dehn扭曲系数之间的关系。具体而言，我们表明，排名的Heegaard Floer同源的3-流形界的分数德恩扭曲系数的monodromy的任何其开卷分解与连接绑定的绝对值。我们证明了这一点，表明的秩的Floer同源边界平行的右或左德恩扭转必要添加到一个表面的自同构，以保证相关的接触流形是紧或overtwisted，分别给出了界限。通过检查分支的双重覆盖，我们还表明，一个链接的Khovanov同源性的秩的边界分数德恩扭曲系数的奇链辫子的代表。
We establish a relationship between Heegaard Floer homology and the fractional Dehn twist coefficient of surface automorphisms. Specifically, we show that the rank of the Heegaard Floer homology of a 3-manifold bounds the absolute value of the fractional Dehn twist coefficient of the monodromy of any of its open book decompositions with connected binding. We prove this by showing that the rank of Floer homology gives bounds for the number of boundary parallel right or left Dehn twists necessary to add to a surface automorphism to guarantee that the associated contact manifold is tight or overtwisted, respectively. By examining branched double covers, we also show that the rank of the Khovanov homology of a link bounds the fractional Dehn twist coefficient of its odd-stranded braid representatives.