论文标题
Instanton和拉紧叶的深度
Instanton and the depth of taut foliations
论文作者
论文摘要
Kronheimer和Mrowka引入了缝合的Instanton Floer同源性。在本文中，我们证明，对于消失的第二个同源性，对于缩减平衡的缝合歧管，缝合的intsanton floer同源性的尺寸为所有可能的拉紧叶子的最小深度提供了一个平衡的缝合式歧管的最小深度。可以将同样的论点适应单调甚至Heegaard浮动设置，这为Juhasz的一个猜想提供了部分答案。使用Instanton Floer同源性的性质，在结中，我们可以构建一个具有界深度的绷紧叶子，并提供有关结基本组的表示形式的一些信息。这表明了表示形式的神秘关系和结上的一些小深度繁殖，并为克朗海默和莫洛卡的猜想提供了部分答案。
Sutured instanton Floer homology was introduced by Kronheimer and Mrowka. In this paper, we prove that for a taut balanced sutured manifold with vanishing second homology, the dimension of the sutured instanton Floer homology provides a bound on the minimal depth of all possible taut foliations on that balanced sutured manifold. The same argument can be adapted to the monopole and even the Heegaard Floer settings, which gives a partial answer to one of Juhasz's conjectures. Using the nature of instanton Floer homology, on knot complements, we can construct a taut foliation with bounded depth, given some information on the representation varieties of the knot fundamental groups. This indicates a mystery relation between the representation varieties and some small depth taut foliations on knot complements, and gives a partial answer to one of Kronheimer and Mrowka's conjecture.
