论文标题
打结浮子同源性的Upsilon扭转功能
An Upsilon torsion function for knot Floer homology
论文作者
论文摘要
Heegaard浮子理论产生与结相关的链络合物。这种复合物被视为多项式环上的模块，产生了扭转不变的，这些扭转不变，对结之间的恢复性提供了约束。例如，juhasz，Miller和Zemke使用扭转不变式来束缚局部最大值和最小值的数量。 Gong和Marengon定义了相关的扭转不变，并将其用于研究不可取向的结率。 在本文中，我们定义了Heegaard漂浮扭转的一个参数家族，该参数不变性不变，该扭矩不变型在间隔[0,2]上定义了分段线性函数。我们将其称为Upsilon扭转功能；它与Ozsvath，Stipsicz和Szabo定义的Heegaard Floer Upsilon函数密切相关。自然而然地，这种Upsilon扭转功能在Juhasz-Miller-Zemke与不变性和Gong-Marengon不变性之间进行了插值。除了在结中界限局部最大值和最小值的数量外，Upsilon扭转功能还提供了与结之间的Gordian距离有关的新障碍物。
Heegaard Floer theory produces chain complexes associated to knots. Viewed as modules over polynomial rings, such complexes yield torsion invariants that offer constraints on cobordisms between knots. For instance, Juhasz, Miller and Zemke used torsion invariants to bound the number of local maxima and minima in cobordisms between pairs of knots. Gong and Marengon defined a related torsion invariant and used it to study nonorientable knot cobordisms. In this paper we define a one parameter family of Heegaard Floer torsion invariants that yields a piecewise linear function defined on the interval [0,2]. We call this the Upsilon torsion function; it is closely related to the Heegaard Floer Upsilon function defined by Ozsvath, Stipsicz and Szabo. In a natural way, this Upsilon torsion function interpolates between the Juhasz-Miller-Zemke invariant and the Gong-Marengon invariant. In addition to bounding the number of local maxima and minima in knot cobordisms, the Upsilon torsion function provides new obstructions related to the Gordian distance between knots.
