标题： Kashaev签名猜想的证明 显示英文标题

标题： A Proof of the Kashaev Signature Conjecture

摘要： 2018年，Kashaev引入了一个图示链接不变量，该不变量被猜想为Levine-Tristram签名的两倍。 如果该猜想成立，将提供一种简单的方法，通过取与相应链接图相关的实对称矩阵的签名来计算链接的Levine-Tristram签名。 本文使用Levine-Tristram签名在有向链接及其反向的不相交并集上的Seifert曲面定义来证明该猜想。 该证明还揭示了另一个关于Alexander多项式的公式。 显示英文摘要

摘要： In 2018 Kashaev introduced a diagrammatic link invariant conjectured to be twice the Levine-Tristram signature. If true, the conjecture would provide a simple way of computing the Levine-Tristram signature of a link by taking the signature of a real symmetric matrix associated with a corresponding link diagram. This paper establishes the conjecture using the Seifert surface definition of the Levine-Tristram signature on the disjoint union of an oriented link and its reverse. The proof also reveals yet another formula for the Alexander polynomial.