The Jones Polynomial from a Goeritz Matrix

Joe Boninger

doi:10.1112/blms.12753

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arXiv · 2110.03082

The Jones Polynomial from a Goeritz Matrix

Joe Boninger

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Abstract

We give an explicit algorithm for calculating the Kauffman bracket of a link diagram from a Goeritz matrix for that link. Further, we show how the Jones polynomial can be recovered from a Goeritz matrix when the corresponding checkerboard surface is orientable, or when more information is known about its Gordon-Litherland form. In the process we develop a theory of Goeritz matrices for cographic matroids, which extends the bracket polynomial to any symmetric integer matrix. We place this work in the context of links in thickened surfaces.

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Joe Boninger. 2021-10-06. The Jones Polynomial from a Goeritz Matrix. https://doi.org/10.1112/blms.12753

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