拱形之和的托拉克斯迹零 SU(2) 字符变型

如果一个链接 $L$ 可以沿着一个与 $L$ 在4个点相交的2个球分解成两个分支 $T\cup_{S^2} S$ 的并集，那么托拉克斯在称为枕垫盒子 (pillowcase) 的空间中进行的托拉克斯的扰动迹零 SU(2) 字符变型的交点形成了一组生成器，用于克劳姆内尔和莫罗卡的简化单点同伦, $I^\natural$。卡扎斯 (Cazassus)、赫拉德 (Herald)、Kirk 和 Kotelskiy conjectured that with the addition of bounding cochains, the differential of $I^\natural$ can be recovered from these Lagrangians as well. This article gives a method to compute the perturbed character variety for a large class of tangles using cut-and-paste methods. In particular, given two tangles, $T$ and $S$, Conway defines the tangle sum $T+S$. Given the character varieties of $T$ and $S$, we show how to construct the perturbed character variety of $T+S$. This is done by first studying the perturbed character variety of a certain tangle $C_3$ properly embedded in $S^3$ with 3 balls removed. Using these results, we prove a nontriviality result for the bounding cochains in the conjecture of Cazassus, Herald, Kirk, and Kotelskiy.