Given a connected cobordism between two knots in the 3‐sphere, our main result is an inequality involving torsion orders of the knot Floer homology of the knots, and the number of local maxima and the genus of the cobordism. This has several topological applications: The torsion order gives lower bounds on the bridge index and the band‐unlinking number of a knot, the fusion number of a ribbon knot, and the number of minima appearing in a slice disk of a knot. It also gives a lower bound on the number of bands appearing in a ribbon concordance between two knots. Our bounds on the bridge index and fusion number are sharp for $T_{p,q}$ and $T_{p,q}\#{\overline{T}}_{p,q}$, respectively. We also show that the bridge index of $T_{p,q}$ is minimal within its concordance class.

中文翻译：

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Floer同源性中的结肋螺旋，桥索引和扭转

给定3球中两个结之间的关联的cobordism，我们的主要结果是不等式，涉及knots结的Floer同源结的扭阶，局部最大值的数量和cobordism的属。这具有几种拓扑应用程序：扭转顺序为桥索引和结的带解链数，带状结的融合数以及在结的切片盘中出现的最小值提供了下限。它还为出现在两个结之间的色带一致性中的波段数提供了一个下限。我们在桥索引和融合数上的界限对于${Ť}_{p，q}$ 和 ${Ť}_{p，q}＃{\overline{Ť}}_{p，q}$， 分别。我们还表明，${Ť}_{p，q}$ 在其和合类中是最小的。