The Gordon-Litherland pairing and its many applications

Abstract

Gordon and Litherland's paper $\textit{On the Signature of a link}$ introduced a bilinear form that simultaneously unifies both the quadratic forms of Trotter and Goeritz. This remarkable pairing of combinatorics and topology has had widespread application in low-dimensional topology. In this expository note, we give a picture proof (via Kirby diagrams) of their main result and discuss the numerous ways their theorem has been put to good use.