Colored Triple Linking Number

Abstract

In an important work, Cimasoni and Florens introduced the notion of a colored link (literally a link whose components have been grouped together by colors). These allow one to define new link invariants by treating components of a single color like they are a single component. In this project, we consider the so-called triple linking number. This invariant can be defined in terms of the intersections of a collections of surfaces bounded by that link. Our new invariant can be used to prove that certain colored links are not boundary links – meaning that any surfaces bounded by their colored sublinks must intersect each other.