论文标题
阻塞还原手术：切片属和厚度边界
Obstructing Reducible Surgeries: Slice Genus and Thickness Bounds
论文作者
论文摘要
在本文中，我们研究了$ s^3 $的结上的可还原手术。我们开发了L空间结的厚度边界，这些结可以接受可减少的手术，并在切片属上的下限，用于接纳可减少手术的一般结。 L空间结的厚度边界使我们能够完成对薄结的电缆猜想的验证，这主要是在\ cite {dey21b}中进行的。我们还提供了一个新的上限，以减少用于纤维，双曲线打结的坡度以及多个减速斜率以进行切片的斜坡。我们的技术涉及Heegaard Floer同源性的$ d $ invariants和映射锥形配方。
In this paper, we study reducible surgeries on knots in $S^3$. We develop thickness bounds for L-space knots that admit reducible surgeries, and lower bounds on the slice genus for general knots that admit reducible surgeries. The L-space knot thickness bounds allow us to finish off the verification of the Cabling Conjecture for thin knots, which was mostly worked out in \cite{DeY21b}. We also provide a new upper bound on reducing slopes for fibered, hyperbolic slice knots and on multiple reducing slopes for slice knots. Our techniques involve the $d$-invariants and mapping cone formula from Heegaard Floer homology.
