Name
Abstract | ||
|---|---|---|
Our goal is to compute the minimal-order recurrence of the colored Jones polynomial of the 7(4) knot, as well as for the first four double twist knots. As a corollary, we verify the AJ Conjecture for the simplest knot 7(4) with reducible nonabelian SL(2, C) character variety. To achieve our goal, we use symbolic summation techniques of Zeilberger's holonomic systems approach and an irreducibility criterion for q-difference operators. For the latter we use an improved version of the qHyper algorithm of Abramov-Paule-Petkovsek to show that a given q-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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.2140/agt.2013.13.3261 | ALGEBRAIC AND GEOMETRIC TOPOLOGY |
Keywords | Field | DocType |
$q$–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, $7_4$ | Topology,Combinatorics,Algebra,Irreducibility,Skein relation,Knot theory,Knot (mathematics),Knot (unit),Knot invariant,Mathematics,Trefoil knot,Quantum invariant | Journal |
Volume | Issue | ISSN |
13 | 6.0 | 1472-2739 |
Citations | PageRank | References |
1 | 0.37 | 12 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stavros Garoufalidis | 1 | 12 | 5.07 |
| Christoph Koutschan | 2 | 104 | 20.29 |