Infinitely many two-variable generalisations of the Alexander–Conway polynomial

We show that the Alexander-Conway polynomial $Δ$ is obtainable via a particular one-variable reduction of each two-variable Links–Gould invariant $L G^{m, 1}$ , 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 $L G^{m, 1}$ does not satisfy a second-order characteristic identity unless $m = 1$ . To demonstrate that the one-variable reduction of $L G^{m, 1}$ satisfies the defining skein relation of $Δ$ , we evaluate the kernel of a quantum trace.

PDF Access Denied

Warning: We have not been able to recognize your IP address 47.88.87.18 as that of a subscriber to this journal. Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form.

Or, visit our subscription page for instructions on purchasing a subscription. You may also contact us at contact@msp.org or by using our contact form.

Or, you may purchase this single article for USD 29.95:

Keywords

link, knot, Alexander-Conway polynomial, quantum superalgebra, Links–Gould link invariant

Mathematical Subject Classification 2000

Primary: 57M25, 57M27

Secondary: 17B37, 17B81

References

Forward citations

Publication

Received: 21 January 2005

Revised: 14 April 2005

Accepted: 28 April 2005

Published: 22 May 2005

Authors

David De Wit
Department of Mathematics The University of Queensland 4072 Brisbane Australia

Atsushi Ishii


Jon Links
Department of Mathematics The University of Queensland 4072 Brisbane Australia

Volume 5, issue 1 (2005)

David De Wit, Atsushi Ishii and Jon Links

Abstract