On the Analytic Properties of the z-Coloured Jones Polynomial

Details On the Analytic Properties of the z-Coloured Jones Polynomial On the Analytic Properties of the z-Coloured Jones Polynomial

2003-10-24

arxiv.org/abs/math/0310394v3

Journal of Knot Theory and Its Ramifications,Vol. 14, No. 4 (June 2005),435-466

Mathematics

Quantum Algebra

Expanded version 39 pages 8 figures

Scientific paper

We analyse the possibility of defining complex valued Knot invariants associated with infinite dimensional unitary representations of $SL(2,R)$ and the Lorentz Group taking as starting point the Kontsevich Integral and the notion of infinitesimal character. This yields a family of knot invariants whose target space is the set of formal power series in $C$, which contained in the Melvin-Morton expansion of the coloured Jones polynomial. We verify that for some knots the series have zero radius of convergence and analyse the construction of functions of which this series are asymptotic expansions by means of Borel re-summation. Explicit calculations are done in the case of torus knots which realise an analytic extension of the values of the coloured Jones polynomial to complex spins. We present a partial answer in the general case.

Affiliated with

Also associated with

No associations

Rating

On the Analytic Properties of the z-Coloured Jones Polynomial does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Analytic Properties of the z-Coloured Jones Polynomial, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Analytic Properties of the z-Coloured Jones Polynomial will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-342705