  We use recent progress on Chern-Simons gauge theory in three dimensions [18]
to give explicit, closed form formulas for the star product on some functions
on the affine space ${\mathcal A}(\Sigma)$ of (smooth) connections on the
trivialized principal $G$-bundle on a compact, oriented two manifold $\Sigma.$
These formulas give a close relation between knot invariants, such as the
Kauffman bracket polynomial, and the Jones and HOMFLY polynomials, arising in
Chern Simons gauge theory, and deformation quantization of ${\mathcal
A}(\Sigma).$ This relation echoes the relation between the manifold invariants
of Witten [20] and Reshetikhin-Turaev [16] and {\em geometric} quantization of
this space (or its symplectic quotient by the action of the gauge group). In
our case this relation arises from explicit algebraic formulas arising from the
(mathematically well-defined) functional integrals of [18].
