论文标题
辫子，纤维结和一致性问题
Braids, fibered knots, and concordance questions
论文作者
论文摘要
给定$ s^3 $的结，可以通过两种不同的方式将表面差异化。首先，可以用辫子表示$ s^{3} $中的任意结，可以将其视为刺穿磁盘的差异性。其次，如果结纤维，也就是说，如果其补体纤维超过$ s^1 $，则可以考虑纤维的单肌。可以询问这些表面差异的特性在多大程度上决定了相应结的拓扑特性。在本文中，我们从辫子的角度和纤维结的角度收集了观察，猜想和问题，以解决这一问题。我们特别关注探索表面差异性的特性是否与打结（例如切片属）的四维拓扑特性有关。
Given a knot in $S^3$, one can associate to it a surface diffeomorphism in two different ways. First, an arbitrary knot in $S^{3}$ can be represented by braids, which can be thought of as diffeomorphisms of punctured disks. Second, if the knot is fibered -- that is, if its complement fibers over $S^1$ -- one can consider the monodromy of the fibration. One can ask to what extent properties of these surface diffeomorphisms dictate topological properties of the corresponding knot. In this article we collect observations, conjectures, and questions addressing this, from both the braid perspective and the fibered knot perspective. We particularly focus on exploring whether properties of the surface diffeomorphisms relate to four-dimensional topological properties of knots such as the slice genus.
