FoCM 2014 conference

Workshop B7 - Symbolic Analysis

December 16, 17:00 ~ 17:25 - Room C21

## $q$-shift operators in knot theory

### Christoph Koutschan

### RICAM, Austrian Academy of Sciences, Austria - christoph.koutschan@ricam.oeaw.ac.at

In knot theory, the colored Jones function is a knot invariant which is an infinite sequence of Laurent polynomials. Through its definition by state sums it is known to be q-holonomic, i.e., to satisfy a linear recurrence of the form $c_d f_{n+d} + \dots + c_0 f_n = 0$, $c_d \neq 0$, whose coefficients $c_0,\dots,c_d$ are bivariate polynomials in $q$ and $q^n$. We discuss how symbolic computation supports the investigation of this knot invariant.

Joint work with Stavros Garoufalidis (Georgia Tech).