English

On Conway's potential function for colored links

Geometric Topology 2016-05-03 v2

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 PnBn\mathbb P_nB_n, where BnB_n is a braid group and Pn\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.

Keywords

Cite

@article{arxiv.1407.3081,
  title  = {On Conway's potential function for colored links},
  author = {Boju Jiang},
  journal= {arXiv preprint arXiv:1407.3081},
  year   = {2016}
}
R2 v1 2026-06-22T05:01:42.929Z