Research on representation theoretic structures of unknot detectors

本文主要研究非结检测器的表示论结构。特别地，我们着重研究了特征标簇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，其零轨迹给出集合S0（K）。应用多项式，我们发现了一个过滤的S0（K），每个过滤器给出了一个结不变。这一事实揭示了S0（K）与阿贝尔结接触同调之间的关系。这些研究中所使用的方法也可以应用于确定素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.