|
|||||
|
|
|
|
|
|
|
|
|
Irreducibility of
$q$–difference operators and the knot $7_4$
Stavros Garoufalidis and Christoph Koutschan |
|
Algebraic & Geometric Topology 13 (2013) 3261–3286
|
Abstract |
|
Our goal is to compute the minimal-order recurrence of the colored Jones polynomial of the knot, as well as for the first four double twist knots. As a corollary, we verify the AJ Conjecture for the simplest knot with reducible nonabelian character variety. To achieve our goal, we use symbolic summation techniques of Zeilberger’s holonomic systems approach and an irreducibility criterion for –difference operators. For the latter we use an improved version of the qHyper algorithm of Abramov–Paule–Petkovšek to show that a given –difference operator has no linear right factors. En route, we introduce exterior power Adams operations on the ring of bivariate polynomials and on the corresponding affine curves. |
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
$q$–holonomic module, $q$–holonomic sequence, creative
telescoping, irreducibility of $q$–difference operators,
factorization of $q$–difference operators, qHyper, Adams
operations, quantum topology, knot theory, colored Jones
polynomial, AJ conjecture, double twist knot, $7_4$
|
Mathematical Subject Classification 2010
Primary: 57N10
Secondary: 57M25, 33F10, 39A13
|
References |
Publication
Received: 26 November 2012
Accepted: 30 April 2013
Published: 10 October 2013
|
Authors |
| Stavros Garoufalidis | |
| School of Mathematics Georgia Institute of Technology 686 Cherry Street Atlanta, GA 30332-0160 USA |
|
| http://www.math.gatech.edu/~stavros | |
| Christoph Koutschan | |
| Johann Radon Institute for
Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences Altenberger Straße 69 A-4040 Linz Austria |
|
| http://www.koutschan.de | |
|
