On Conway's potential function for colored links

Boju Jiang

doi:10.1007/s10114-015-4428-9

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arXiv · 1407.3081

On Conway's potential function for colored links

Boju Jiang

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Abstract

The Conway potential function (CPF) for colored links is a convenient version of the multi-variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway's `smoothing of crossings' is not in the axioms. The proof uses a reduction scheme in a twisted group-algebra $\mathbb P_nB_n$, where $B_n$ is a braid group and $\mathbb P_n$ is a domain of multi-variable rational fractions. The proof does not use computer algebra tools. An interesting by-product is a characterization of the Alexander-Conway polynomial of knots.

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Boju Jiang. 2014-07-11. On Conway's potential function for colored links. https://doi.org/10.1007/s10114-015-4428-9

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