论文标题
Seiberg-Witten理论的结结一致性不变性和4个manifolds中的切片属界限
Knot concordance invariants from Seiberg-Witten theory and slice genus bounds in 4-manifolds
论文作者
论文摘要
我们构建了一个新的结成结合一致的家族，不变性$θ^{（q）}（k）$，其中$ q $是质量数字。我们的不变式是从作者和Hekmati建造的Equivariant Seiberg-Witten-loer同谋获得的，该学位适用于$ Q $ Q $ cyclic Cover，$ s^3 $以$ k $的分支为$ s^3 $。在情况下，$ q = 2 $，我们的不变$θ^{（2）}（k）$与HOM和WU定义的结Floer同源性不变$ν^+（k）$共享许多相似之处。我们的不变量$θ^{（q）}（k）$在任何平滑，正确嵌入，具有琐碎的表面上的$ k $的属性上给出了下限，该$ 4 $ -4 $ -Manifold带有边界$ s^3 $。
We construct a new family of knot concordance invariants $θ^{(q)}(K)$, where $q$ is a prime number. Our invariants are obtained from the equivariant Seiberg-Witten-Floer cohomology, constructed by the author and Hekmati, applied to the degree $q$ cyclic cover of $S^3$ branched over $K$. In the case $q=2$, our invariant $θ^{(2)}(K)$ shares many similarities with the knot Floer homology invariant $ν^+(K)$ defined by Hom and Wu. Our invariants $θ^{(q)}(K)$ give lower bounds on the genus of any smooth, properly embedded, homologically trivial surface bounding $K$ in a definite $4$-manifold with boundary $S^3$.
