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引用次数: 0
摘要
我们考虑 4 球中边界为 3 球中固定结的连通表面集。我们将两个表面之间的稳定距离定义为最小 g $g$,即我们可以通过最多 g $g$ 属性的表面进行稳定和失稳,从一个表面到达另一个表面。同样,我们认为两个同属曲面之间的双点距离是连接这两个曲面的所有正则同调中出现的最大双点数目的最小值。对于许多使用 Heegaard Floer 同调定义的协整不变量,我们为一对曲面构建了类似的不变量。我们证明,这些变量给出了稳定距离和双点距离的下限。我们通过证明全无穷结弗洛尔复数上的迹公式,以及确定一个结与自身的连通和的自动变形对结弗洛尔同调的作用,计算出一些变形纺切片盘对的不变量。我们利用我们的不变式找到了相对于本文所考虑的许多度量具有任意大距离的片盘对。我们还回答了柯比问题列表中问题 1.105 (B) 的切片盘类似问题,证明了非 0 协方切片盘的存在。
Stabilization distance bounds from link Floer homology
We consider the set of connected surfaces in the 4-ball with boundary a fixed knot in the 3-sphere. We define the stabilization distance between two surfaces as the minimal such that we can get from one to the other using stabilizations and destabilizations through surfaces of genus at most . Similarly, we consider a double-point distance between two surfaces of the same genus that is the minimum over all regular homotopies connecting the two surfaces of the maximal number of double points appearing in the homotopy. To many of the concordance invariants defined using Heegaard Floer homology, we construct an analogous invariant for a pair of surfaces. We show that these give lower bounds on the stabilization distance and the double-point distance. We compute our invariants for some pairs of deform-spun slice disks by proving a trace formula on the full infinity knot Floer complex, and by determining the action on knot Floer homology of an automorphism of the connected sum of a knot with itself that swaps the two summands. We use our invariants to find pairs of slice disks with arbitrarily large distance with respect to many of the metrics we consider in this paper. We also answer a slice-disk analog of Problem 1.105 (B) from Kirby's problem list by showing the existence of non-0-cobordant slice disks.
期刊介绍:
The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal.
The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.