Generalised Biracks and the Birack Polynomial Invariant

Andrew Bartholomew; Roger Fenn; Louis Kauffman

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arXiv · 2503.08268

Generalised Biracks and the Birack Polynomial Invariant

Andrew Bartholomew·Roger Fenn·Louis Kauffman

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Abstract

We generalise the finite biquandle colouring invariant to a polynomial invariant based on labelling a knot diagram with a finite birack that reduces to the biquandle colouring invariant in that case. The polynomial is an invariant of a class of knot theories amenable to a generalisation of theorem of Trace on regular homotopy. We take the opportunity to reprise the relevant generalised knot theory and the theory of generalised biracks in the light of this work and recent developments.

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Andrew Bartholomew, Roger Fenn, Louis Kauffman. 2025-03-11. Generalised Biracks and the Birack Polynomial Invariant. https://arxiv.org/abs/2503.08268

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