论文标题
积分二元二元形式与结多项式之间的新型联系
A novel connection between integral binary quadratic forms and knot polynomials
论文作者
论文摘要
我们在代数数理论与结理论之间建立了一种新颖的联系。我们表明，积分二进制二进制二进制形式的等价类别的差异$ t^2-4 $（对于$ t \ neq \ pm 2 $）等于$ \ mathbb {s}^3 $中的同位素类别链接的数量（根据规定的$ t $ t三个类别链接noctical novariants的$ t $）。平等源于整体二进制二进制形式之间的天然代数对应关系（$ t \ neq \ pm 2 $的判别$ t^2-4 $）和辫子索引的链接类别最多三种。特别是，某些二次数字字段的类数量精确地衡量了亚历山大/琼斯多项式以区分辫子索引的非同位素链接的失败。
We establish a novel connection between algebraic number theory and knot theory. We show that the number of equivalence classes of integral binary quadratic forms of discriminant $t^2 - 4$ (for $t\neq \pm 2$) is equal to the number of isotopy classes of links in $\mathbb{S}^3$ with prescribed values (depending on $t$) of three classical link invariants. The equality arises from a natural algebraic correspondence between integral binary quadratic forms (of discriminant $t^2 - 4$ for $t\neq \pm 2$) and isotopy classes of links of braid index at most three. In particular, the class numbers of certain quadratic number fields precisely measure the failure of the Alexander/Jones polynomial to distinguish non-isotopic links of braid index at most three.
