  Using a two component $SL(2) $ isospinor formalism, we study the link between
conifold $T^{\ast}\mathbb{S}^{3}$ and q-deformed non commutative holomorphic
geometry in complex four dimensions. Then, thinking about conifold as a
projective complex three dimension hypersurface embedded in non compact
$WP^{5}(1,-1,1,-1,1,-1) $ space and using conifold local isometries, we study
topological $SL(2) $ gauge theory on $T^{\ast}\mathbb{S}^{3}$ and its
reductions to lower dimension sub-manifolds $T^{\ast}\mathbb{S}^{2}$,
$T^{\ast}\mathbb{S}^{1}$ and their real slices. Projective symmetry is also
used to build a supersymmetric QFT$%_{4}$ realization of these backgrounds.
Extensions for higher dimensions with conifold like properties are explored.
\bigskip \textbf{Key words}: Conifold, q-deformation, non commutative complex
geometry, topological gauge theory. Nambu like background.
