Noncommutative deformation of instantons

We study instanton solutions on noncommutative Euclidean 4-space which are deformations of instanton solutions on commutative Euclidean 4-space. We show that the instanton numbers of these noncommutative instanton solutions coincide with the commutative solutions and conjecture that the instanton number in R4R4 is preserved for general noncommutative deformations. We also study noncommutative deformation of instanton solutions on a T4T4 with twisted boundary conditions.