Quantizations of Character Varieties and Quantum Knot Invariants

Understand

Let G be a simple complex algebraic group and g its Lie algebra.

• We show that the g-Witten-Reshetikhin-Turaev quantum invariants determine a deformation-quantization, C_q[X_G(torus)], of the coordinate ring of the G-character variety of the torus.
• We prove that this deformation is in the direction of the Goldman's bracket.
• Furthermore, we show that every knot K defines an ideal I_K in C_q[X_G(torus)].