Research on representation theoretic structures of unknot detectors

本研究是关于非节点检测器表征理论结构的研究。特别地，我们重点研究了由无迹条件定义的特征标簇X(K)的代数子集S0(K)上的几何结构。在研究中，我们发现了一族多项式，其零点轨迹给出了集合S0(K)。应用多项式，我们找到了S0(K)的一个滤子，每个滤子都给出一个纽结不变量。这一事实揭示了S_0(K)与交换纽结接触同调之间的关系。这些研究中使用的方法也可以用来确定素数纽结的偏序的一些极小元。

This study is concerned with researches on representation theoretic structures of unknot detectors. In particular, we focus on the geometric structures on the algebraic subset S0(K) of the character variety X(K) defined by trace-free condition. In the researches, we found a family of polynomials whose zero-locus gives the set S0(K). Applying the polynomials, we found a filtration of S0(K) each of whose filters gives a knot invariant. This fact reveals a relationship between S0(K) and the abelian knot contact homology. The methods used in these researches can be also applied to determine some minimal elements for a partial ordering of prime knots.