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Representations and the colored Jones polynomial of a torus knot
- Publication Year :
- 2010
-
Abstract
- We show that for a torus knot the SL(2;C) Chern-Simons invariants and the SL(2;C) twisted Reidemeister torsions appear in an asymptotic expansion of the colored Jones polynomial. This suggests a generalization of the volume conjecture that relates the asymptotic behavior of the colored Jones polynomial of a knot to the volume of the knot complement.<br />Comment: 18 pages, 1 figure, submitted to the Proceedings of the workshop "Chern-Simons Gauge Theory: 20 Years After"
- Subjects :
- Mathematics - Geometric Topology
57M27
57M25
57M50
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1001.2680
- Document Type :
- Working Paper