Abstract
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 R 4 is preserved for general noncommutative deformations. We also study noncommutative deformation of instanton solutions on a T 4 with twisted boundary conditions.
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