论文标题
双线性增强不变性
Bilinear Enhancements of Quandle Invariants
论文作者
论文摘要
我们使用类似于Quandle模块的结构增强了定向古典和虚拟结的不变性，但受到符号搜索操作的启发，而不是亚历山大·奎德尔操作。考虑到有限的Quandle $ x $和一个田野上的矢量空间$ v $，$ v $上的一组双线性表格，由$ x $的成对索引，满足某些条件的$ x $，产生新的增强的增强的多项式和多项式价值的不变，这些不变的不变的经典经典和虚拟结和链接。我们提供示例来说明不变性的计算，并表明增强功能是正确的。
We enhance the quandle counting invariants of oriented classical and virtual knots and links using a construction similar to quandle modules but inspired by symplectic quandle operations rather than Alexander quandle operations. Given a finite quandle $X$ and a vector space $V$ over a field, sets of bilinear forms on $V$ indexed by pairs of elements of $X$ satisfying certain conditions yield new enhanced multiset- and polynomial-valued invariants of oriented classical and virtual knots and links. We provide examples to illustrate the computation of the invariants and to show that the enhancement is proper.
