Mathematical Sciences: Connections Between Geometry and LinkPolynomials

希斯尔韦特计划研究经典纽结理论和“迹”多项式不变量理论中几个相互关联的问题。主要任务是寻找新的多项式不变量的内在几何定义。此外，希斯尔韦特将寻求两个琼斯多项式的两个变量推广的改进的组合定义，希望从那里快速地证明这些多项式的存在。在纯粹的几何方面，他将追寻这样一个问题，即链接的交叉数量是否相对于连接和是相加的。

Thistlewaite plans to examine several interconnected problems in classical knot theory and the theory of `trace' polynomial invariants. The principal task is the search for intrinsic geometrical definitions of the new polynomial invariants of links. Also, Thistlewaite will seek improved combinatorial definitions of the two 2-variable generalizations of the Jones polynomial, from which it is hoped that rapid proofs of the existence of these polynomials will materialize. On a purely geometrical front, he will pursue the question as to whether crossing-number of links is additive with respect to connected sum.