Open Access
Translator Disclaimer
2005 Infinitely many two-variable generalisations of the Alexander–Conway polynomial
David De Wit, Atsushi Ishii, Jon Links
Algebr. Geom. Topol. 5(1): 405-418 (2005). DOI: 10.2140/agt.2005.5.405

Abstract

We show that the Alexander-Conway polynomial Δ is obtainable via a particular one-variable reduction of each two-variable Links–Gould invariant LGm,1, where m is a positive integer. Thus there exist infinitely many two-variable generalisations of Δ. This result is not obvious since in the reduction, the representation of the braid group generator used to define LGm,1 does not satisfy a second-order characteristic identity unless m=1. To demonstrate that the one-variable reduction of LGm,1 satisfies the defining skein relation of Δ, we evaluate the kernel of a quantum trace.

Citation

Download Citation

David De Wit. Atsushi Ishii. Jon Links. "Infinitely many two-variable generalisations of the Alexander–Conway polynomial." Algebr. Geom. Topol. 5 (1) 405 - 418, 2005. https://doi.org/10.2140/agt.2005.5.405

Information

Received: 21 January 2005; Revised: 14 April 2005; Accepted: 28 April 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1079.57004
MathSciNet: MR2153122
Digital Object Identifier: 10.2140/agt.2005.5.405

Subjects:
Primary: 57M25, 57M27
Secondary: 17B37, 17B81

Rights: Copyright © 2005 Mathematical Sciences Publishers

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.5 • No. 1 • 2005
MSP
Back to Top