The Multi-variable Affine Index Polynomial

Nicolas Petit

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arXiv · 1909.04159

The Multi-variable Affine Index Polynomial

Nicolas Petit

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Abstract

We define a multi-variable version of the Affine Index Polynomial for virtual links. This invariant reduces to the original Affine Index Polynomial in the case of virtual knots, and also generalizes the version for compatible virtual links recently developed by L. Kauffman. We prove that this invariant is a Vassiliev invariant of order one, and study what happens as we shift the coloring of one or more components.

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Nicolas Petit. 2019-09-09. The Multi-variable Affine Index Polynomial. https://arxiv.org/abs/1909.04159

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