Konferenzvortragsdetails

Konferenz: Kazuo Habiro: Special talks


On certain limits of the reduced colored Jones polynomials

Vortrag von Prof. Dr. Kazuo Habiro
Datum: 13.04.10   Zeit: 15.00 - 17.00   Raum: Y27H46

Abstract: The colored Jones polynomial is defined for a knot and a positive integer $n$ and takes values in the Laurent polynomial ring $Z[q,q^{-1}]$. Dasbach and Lin studied the "head" and "tail" of the colored Jones polynomials. They proved that, up to sign, the last and the first three coefficients of the colored Jones polynomials of an alternating knot converge (i.e., are independent of $n$ with finitely many exceptions), and conjectured that the other coefficients also converge and yield two power series in $q$ and in $q^{-1}$. Let us call these power series the head series and the tail series. In this talk, I consider existence of the head and the tail series for the reduced colored Jones polynomials, which are certain linear combinations of the colored Jones polynomials, taking values in the Laurent polynomial ring. We conjecture that the head and the tail series exist for the reduced colored Jones polynomials for an alternating knot. Moreover, we conjecture that the head (but not the tail) series exist for a positive knot and that all the coefficients are nonnegative. Examples and partial results will also be given.