  Studied are moduli spaces of self dual or anti-self dual connections on
noncommutative 4-manifolds, especially deformation quantization of compact spin
Riemannian 4-manifolds and their isometry groups have 2-torus subgroup. Then
such moduli spaces of irreducible modules associated with highestweights of
compact connected semisimple Lie groups are smooth manifolds with dimension
determined by their weights. This is a generalization of
Atiyah-Hitchin-Singer's classical result as well as Landi-Suijlekom's
noncommutative 4-sphere case.
