8 papers
The computation of the non-commutative generalization of the A-polynomial for the figure-eight knot
Razvan Gelca, Jeremy Sain
The paper contains the computation of the noncommutative A-ideal of the figure-eight knot, a noncommutative generalization of the A-polynomial. We show that if a knot has the same…
A product-to-sum formula for the quantum group of SL(2,C)
Razvan Gelca
The paper exhibits a product-to-sum formula for the observables of a certain quantization of the moduli space of flat SU(2)-connections on the torus. This quantization was defined…
The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial
Razvan Gelca, Jeremy Sain
The noncommutative A-ideal of a knot is a generalization of the A-polynomial, defined using Kauffman bracket skein modules. In this paper we show that any knot that has the same no…
Noncommutative trigonometry and the A-polynomial of the trefoil knot
Razvan Gelca
The paper shows the computation of the noncommutative generalization of the A-polynomial of the trefoil knot. The classical A-polynomial was introduced by Cooper, Culler, Gillet, L…
On the relation between the A-polynomial and the Jones polynomial
Razvan Gelca
In previous joint work with Frohman and Lofaro a noncommutative generalization of the A-polynomial of a knot was introduced, consisting of a finitely generated ideal of polynomials…
On the groupoid of transformations of rigid structures on surfaces
Louis Funar, Razvan Gelca
We prove that the groupoid of transformations of rigid structures on surfaces has a finite presentation as a 2-groupoid establishing a result first conjectured by G.Moore and N.Sei…