Moduli Spaces of Instantons on Noncommutative 4-Manifolds

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 AtiyahHitchin-Singer’s classical result as well as Landi-Suijlekom’s noncommutative 4-sphere case.