The interlace polynomial of binary delta-matroids and link invariants

TL;DR

This paper extends the interlace polynomial from graphs to delta-matroids, proving it satisfies key relations and acts as a finite type invariant for links in 3-spheres, bridging combinatorics and knot theory.

Contribution

It introduces the interlace polynomial for delta-matroids, demonstrating its four-term relation and its role as a finite type invariant for links.

Findings

Interlace polynomial satisfies the four-term relation for delta-matroids.

The polynomial determines a finite type invariant of links in the 3-sphere.

Establishes a connection between delta-matroids and link invariants.

Abstract

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 determines thus a finite type invariant of links in the 3-sphere.