Infinitely many two-variable generalisations of the Alexander-Conway polynomial
Geometric Topology
2014-10-01 v6
Abstract
We show that the Alexander-Conway polynomial Delta is obtainable via a particular one-variable reduction of each two-variable Links-Gould invariant LG^{m,1}, where m is a positive integer. Thus there exist infinitely many two-variable generalisations of Delta. This result is not obvious since in the reduction, the representation of the braid group generator used to define LG^{m,1} does not satisfy a second-order characteristic identity unless m=1. To demonstrate that the one-variable reduction of LG^{m,1} satisfies the defining skein relation of Delta, we evaluate the kernel of a quantum trace.
Cite
@article{arxiv.math/0405403,
title = {Infinitely many two-variable generalisations of the Alexander-Conway polynomial},
author = {David De Wit and Atsushi Ishii and Jon Links},
journal= {arXiv preprint arXiv:math/0405403},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-18.abs.html