论文标题
在单极Lefschetz上有限级差异的数量
On the monopole Lefschetz number of finite order diffeomorphisms
论文作者
论文摘要
让$ k $成为一个积分同源性3-Sphere $ y $的结，而$σ$相应的$ n $ fold循环分支盖。假设$σ$是一个合理的同源性领域（当$ n $是主要功率时，总是这种情况），我们为Lefschetz数量的动作提供了一个公式，覆盖翻译会导致$σ$的减少单极同源性。证明依靠对Seiberg的仔细分析 - 三孔和各种$η$ - invariants的方程式。我们提供了公式的几个应用：（1）我们计算了Seiberg（Witten and Furuta-furuta-ohta-ohta不变性），用于在整体同源物3 spheres上的所有半无半动作的映射Tori； （2）我们为$ s^3 $的结套盖（以琼斯多项式而言）给出了一种新颖的障碍物（就琼斯多项式而言）。 （3）我们提供了一组新的结一致一致性不变性，以支付盖上的单台覆盖层的翻译数量。
Let $K$ be a knot in an integral homology 3-sphere $Y$, and $Σ$ the corresponding $n$-fold cyclic branched cover. Assuming that $Σ$ is a rational homology sphere (which is always the case when $n$ is a prime power), we give a formula for the Lefschetz number of the action that the covering translation induces on the reduced monopole homology of $Σ$. The proof relies on a careful analysis of the Seiberg--Witten equations on 3-orbifolds and of various $η$-invariants. We give several applications of our formula: (1) we calculate the Seiberg--Witten and Furuta--Ohta invariants for the mapping tori of all semi-free actions of $Z/n$ on integral homology 3-spheres; (2) we give a novel obstruction (in terms of the Jones polynomial) for the branched cover of a knot in $S^3$ being an $L$-space; (3) we give a new set of knot concordance invariants in terms of the monopole Lefschetz numbers of covering translations on the branched covers.
