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 , where is a braid group and 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}
}