论文标题
琼斯和亚历山大多项式的全球化是由两个拉格朗日在配置空间中的分级相交构建的
A globalisation of Jones and Alexander polynomials constructed from a graded intersection of two Lagrangians in a configuration space
论文作者
论文摘要
我们考虑了两个与辫子相关的变量中的两个laurent多项式。为了获得链接不变性，我们注意到我们必须通过二次关系进行商品。然后，我们通过拓扑工具证明这种关系足够，并且第一个分级的交叉点给出了琼斯多项式的不变性。这显示了琼斯多项式}的{\ em拓扑模型和一个直接{\ em拓扑证明} \ hspace {0.4mm}，它是一个明确定义的不变性。商中的另一个相交模型证明是琼斯和亚历山大多项式的不变全球化。商环中的这种全球化由亚历山大和琼斯多项式之间的{\ em特定的插值}给出。
We consider two Laurent polynomials in two variables associated to a braid, given by {\em graded intersections} between {\em fixed Lagrangians in configuration spaces}. In order to get link invariants, we notice that we have to quotient by a quadratic relation. Then we prove by topological tools that this relation is sufficient and the first graded intersection gives an invariant which is the Jones polynomial. This shows a {\em topological model for the Jones polynomial} and a direct {\em topological proof}\hspace{0.4mm} that it is a well-defined invariant. The other intersection model in the quotient turns out to be an invariant globalising the Jones and Alexander polynomials. This globalisation in the quotient ring is given by a {\em specific interpolation between the Alexander and Jones polynomials}.
