The Interlace Polynomial of Binary Delta-Matroids and Link Invariants

In this work, we study the interlace polynomial as a generalization of a graph invariant to delta-matroids. We prove that the interlace polynomial satisfies the four-term relation for delta-matroids and thus determines a finite type invariant of links in the $$3$$ -sphere. Using the interlace polynomial, we give a lower bound for the size of the Hopf algebra of binary delta-matroids modulo the $$4$$ -term relations.