The purely cosmetic surgery conjecture is true for the Kinoshita-Terasaka and Conway knot families

The reduced HOMFLY-PT homology for the Conway and the Kinoshita-Terasaka knots

In this paper we compute the reduced HOMFLY-PT homologies of the Conway and the Kinoshita-Terasaka knots and show that they are isomorphic.

Chirally Cosmetic Surgeries on Kinoshita-Terasaka and Conway knot families

In this note, we prove that a nontrivial Kinoshita-Terasaka or Conway knot does not admit chirally cosmetic surgeries, by calculating the finite type invariant of order 3.

Symmetric unions without cosmetic crossing changes

A symmetric union of two knots is a classical construction in knot theory which generalizes connected sum, introduced by Kinoshita and Terasaka in the 1950s. We study this construction for the purpose of finding an infinite family of hyperbolic non-fibered three-bridge knots of constant determinant which satisfy the well-known cosmetic crossing conjecture. This conjecture asserts that the only crossing changes which preserve the isotopy type of a knot are nugatory.

利用Links-Gould不变量得到纽结亏格的下界

A lower bound for the genus of a knot using the Links-Gould invariant

通过研究Links-Gould多项式次数，给出了任意纽结Seifert亏格的下界，改进了Alexander多项式的Seifert不等式，并检测到Kinoshita-Terasaka和Conway纽结的亏格至少为2。

从量子sl_3出发的非阿贝尔化亚历山大多项式

A Non-Abelian Generalization of the Alexander Polynomial from Quantum $\mathfrak{sl}_3$

本文提出一种非阿贝尔化的亚历山大多项式，通过量子sl_3的表示在四次单位根下的构造，建立了一个针对半单李代数的链接不变量，并展示了其与亚历山大多项式的关系。