Analogues of the Gordon–Litherland pairing for other knotted object categories

Develop analogues of the Gordon–Litherland pairing for other categories of knotted objects, specifically spatial graphs, surface-links, and pseudoknots, extending beyond its established form for links in thickened surfaces.

Background

The Gordon–Litherland pairing is a fundamental tool in knot theory providing a bilinear form associated to a spanning surface, with deep connections to link signatures and surface topology. Recent work has extended the pairing to links in thickened surfaces, and this problem seeks to generalize it further to other knotted object categories, including spatial graphs, surface-links, and pseudoknots, thereby broadening its applicability across low-dimensional topology.