Abstract:We consider a family of noncommutative 4-spheres where the deformation is with respect to a 2-torus action. Classically, this corresponds to a Poisson structure on the four-sphere that vanishes on two 2-spheres that connect the north and south poles; these are the fixed points of the torus action. On these noncommutative spheres, we study instantons, i.e. connections with self-dual curvature. It turns out that the (classical) Hopf fibration on the 4-sphere can be deformed to give the structure of a noncommutative principal bundle. Associated to this principal bundle we obtain explicit expressions for the instanton connection.