论文标题
结上的平面同源性和手术
Knot Floer homology and surgery on equivariant knots
论文作者
论文摘要
鉴于订单$ 2 $的等效结$ k $，我们研究了对称性在结式浮子同源性上的诱导动作。我们将这种动作与对称性在$ k $上进行的大型手术的Heegaard浮子同源性的诱导动作联系起来。该手术公式可以被认为是亨德里克斯和马尔伯斯库证明的参与大型手术公式的均等类似物。结果，我们获得了$ s^{3} $和软木的某些双支封面，因此可以通过对调节浮子同源性采取的动作来识别这次纠纷的诱导作用。作为一种应用，我们计算了均等校正项，这些校正项是旋转理性同源性共同体组的广义版本的不变性，并定义了两个结的一致性。我们还计算了对称对称的动作，以$ k $ $ k $的几个等效结。
Given an equivariant knot $K$ of order $2$, we study the induced action of the symmetry on the knot Floer homology. We relate this action with the induced action of the symmetry on the Heegaard Floer homology of large surgeries on $K$. This surgery formula can be thought of as an equivariant analog of the involutive large surgery formula proved by Hendricks and Manolescu. As a consequence, we obtain that for certain double branched covers of $S^{3}$ and corks, the induced action of the involution on Heegaard Floer homology can be identified with an action on the knot Floer homology. As an application, we calculate equivariant correction terms which are invariants of a generalized version of the spin rational homology cobordism group, and define two knot concordance invariants. We also compute the action of the symmetry on the knot Floer complex of $K$ for several equivariant knots.
