论文标题
框架的Instanton同源和一致性
Framed instanton homology and concordance
论文作者
论文摘要
我们使用Fraded Instanton同源性定义了两个结的一致性。这些不变的$ν^\ sharp $和$τ^\ sharp $在切片属和最大自链数字上提供了界限，而后者是一种一致性同构，在所有已知案例中都与$τ$不变在Heegaard Floer同源物中一致。我们使用$ν^\ sharp $和$τ^\ sharp $来计算所有非零理性dehn手术的框架同源性，上面是：35个非平凡的质子结中的20个通过8个十字架，无限的扭曲和椒盐脆饼结的家族，以及Instanton L空间结；在霍奇森（Hodgson）的前20个封闭双曲线歧管中，有19个人口普查。在另一个应用程序中，我们确定结的电缆何时是Instanton L空间结。最后，我们讨论了从Odd Khovanov同源性到分支双层覆盖物的构件同源性的频谱序列的应用，以及$τ^\ Sharp $和$τ$在属-2突变下的行为。
We define two concordance invariants of knots using framed instanton homology. These invariants $ν^\sharp$ and $τ^\sharp$ provide bounds on slice genus and maximum self-linking number, and the latter is a concordance homomorphism which agrees in all known cases with the $τ$ invariant in Heegaard Floer homology. We use $ν^\sharp$ and $τ^\sharp$ to compute the framed instanton homology of all nonzero rational Dehn surgeries on: 20 of the 35 nontrivial prime knots through 8 crossings, infinite families of twist and pretzel knots, and instanton L-space knots; and of 19 of the first 20 closed hyperbolic manifolds in the Hodgson--Weeks census. In another application, we determine when the cable of a knot is an instanton L-space knot. Finally, we discuss applications to the spectral sequence from odd Khovanov homology to the framed instanton homology of branched double covers, and to the behaviors of $τ^\sharp$ and $τ$ under genus-2 mutation.
