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MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics



Funded by The Danish National Research Foundation
Geometric Mathematical Physics Seminar
Wednesday, 20 August 2003, at 16:15 in AUD D3
Gregor Masbaum
Paris VII
On the colored Jones polynomial of twist knots

Abstract
Habiro has shown using quantum groups that the colored Jones polynomial of a knot has a so-called cyclotomic expansion. This expansion is useful for studying the volume conjecture. It is also an important tool for constructing Habiro's universal $fsl_2$ invariant of integral homology $3$-spheres. Explicit computations of this expansion, however, existed only for a few knots. In this talk I will explain how to use skein theory to compute the cyclotomic expansion for twist knots. This is an infinite series of knots including the trefoil and the figure eight knot, and my formulas generalize previously known formulas of Habiro and Le for those two knots.

Contact person:Jørgen Ellegaard Andersen.