论文标题
YAMADA多项式和相关链接$θ$ -CURVES
Yamada Polynomial and associated link of $θ$-curves
论文作者
论文摘要
V. F. R. Jones点燃的结和链接多项式不变的发现导致空间图的多项式不变性。 Yamada多项式是这样不变的之一，经常用于实际区分空间图。尤其是对于$θ$ curves，多项式是标准化后的环境同位素不变。另一方面，对于每个$θ$ -Curve，一个3组分链接可以作为环境同位素不变。关联链接的好处是，链接的不变性可以用作$θ$ curves的不变性。 在本文中，我们调查了$θ$ curves的归一化Yamada多项式与其相关链接的琼斯多项式之间的关系，并表明这两个多项式对于Brunnian $θ$ curves是合理的。就我们的目的而言，观察到空间图的Jaeger多项式，其专业化相当于Yamada的多项式。
The discovery of polynomial invariants of knots and links, ignited by V. F. R. Jones, leads to the formulation of polynomial invariants of spatial graphs. The Yamada polynomial, one of such invariants, is frequently utilized for practical distinguishment of spatial graphs. Especially for $θ$-curves, the polynomial is an ambient isotopy invariant after a normalization. On the other hand, to each $θ$-curve, a 3-component link can be associated as an ambient isotopy invariant. The benefit of associated links is that invariants of links can be utilized as invariants of $θ$-curves. In this paper we investigate the relation between the normalized Yamada polynomial of $θ$-curves and the Jones polynomial of their associated links, and show that the two polynomials are equivalent for brunnian $θ$-curves as a corollary. For our purpose the Jaeger polynomial of spatial graphs is observed, a specialization of which is equivalent to the Yamada polynomial.
