论文标题
Seiberg-witten的浮子K理论和循环群体在具有边界的旋转四个manifolds上
Seiberg-Witten Floer K-theory and cyclic group actions on spin four-manifolds with boundary
论文作者
论文摘要
给定一个配备了$ \ mathbb {z}/m $ y $ y $ y $的旋转理性同源性球，我们使用seiberg- witten方程来定义不变的$κ（y）$的等效性，以\ cite {man14}的形式从一个有限的子集成中的形式中，从$ \ text {pin}（2）$和$ \ mathbb {z}/m $。主要定理由等效的10/8-Tht类型不等式组成，用于旋转同源性领域之间的自旋模化恢复。我们提供了打结一致性的应用，为扩展循环群的旋转填充物的障碍物提供了障碍，并且通过取分支盖，我们获得了刺穿的4个manifolds中的结属边界。在某些情况下，这些界限足以确定$ \ Mathbb {C} p^{2} \＃\＃\ Mathbb {c} p^{2} $，$ s^{2} {2} {2} \ times s^{2} {2} {2} {2} {2} $ s}的相对属的相对属。 $ \ mathbb {c} p^{2} \＃s^{2} \ times s^{2} $和同型$ k3 $ surfaces。
Given a spin rational homology sphere $Y$ equipped with a $\mathbb{Z}/m$-action preserving the spin structure, we use the Seiberg--Witten equations to define equivariant refinements of the invariant $κ(Y)$ from \cite{Man14}, which take the form of a finite subset of elements in a lattice constructed from the representation ring of a twisted product of $\text{Pin}(2)$ and $\mathbb{Z}/m$. The main theorems consist of equivariant relative 10/8-ths type inequalities for spin equivariant cobordisms between rational homology spheres. We provide applications to knot concordance, give obstructions to extending cyclic group actions to spin fillings, and via taking branched covers we obtain genus bounds for knots in punctured 4-manifolds. In some cases, these bounds are strong enough to determine the relative genus for a large class of knots within certain homology classes in $\mathbb{C} P^{2}\#\mathbb{C} P^{2}$, $S^{2}\times S^{2}\# S^{2}\times S^{2}$, $\mathbb{C} P^{2}\# S^{2}\times S^{2}$, and homotopy $K3$ surfaces.
