The Jones Polynomial from a Goeritz Matrix

Joe Boninger (CUNY)

The Jones polynomial holds a central place in knot theory, but its topological meaning is not well understood—it remains an open problem, posed by Atiyah, to give a three-dimensional interpretation of the polynomial. In this talk, we’ll share an original construction of the Jones polynomial from a Goeritz matrix, a combinatorial object with topological significance. In the process we extend the Kauffman bracket to any symmetric, integer matrix, with applications to links in thickened surfaces. Matroid theory plays a role.