Quantizations of Character Varieties and Quantum Knot Invariants
| dc.creator | Sikora, Adam S. | |
| dc.date | 2008-07-07 | |
| dc.date | 2008-07-18 | |
| dc.date.accessioned | 2026-07-07T09:50:52Z | |
| dc.date.available | 2026-07-07T09:50:52Z | |
| dc.description | Let G be a simple complex algebraic group and g its Lie algebra. We show that the g-Witten-Reshetikhin-Turaev quantum invariants determine a deformation-quantization, C_q[X_G(torus)], of the coordinate ring of the G-character variety of the torus. We prove that this deformation is in the direction of the Goldman's bracket. Furthermore, we show that every knot K defines an ideal I_K in C_q[X_G(torus)]. We conjecture that the homomorphism C_q[X_G(torus)] -> C[X_G(torus)], q -> 1, maps I_K to the ideal whose radical is the kernel of the map C[X_G(torus)] -> C[X_G(S^3 K)]. This conjecture is related to AJ-conjecture for sl(2,\C). The results of this paper are inspired by the theory of q-holonomic relations between quantum invariants of Garoufalidis and Le. Along the way, we disprove Conjecture 2 in Le's "The Colored Jones and the A-polynomial of Two-Bridge knots". | |
| dc.description | 17 pages, 1 picture | |
| dc.identifier | https://arxiv.org/abs/0807.0943 | |
| dc.identifier | http://arxiv.org/abs/0807.0943 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165090 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M27,53D55,46L65 | |
| dc.title | Quantizations of Character Varieties and Quantum Knot Invariants | |
| dc.type | text |