Comment on noncommutative deformation of instantons (Q1029473)

This paper deals with the noncommutative deformation of instantons. Recently, Y. Maeda and A. Sako discussed the case of \(\mathbb R^4\) and argued that, on a 4-torus, the noncommutative deformation of instantons should alter the instanton numbers for an arbitrary noncommutativity parameter. In this work, the author proves that it is not the case for \(U(N^2)\). The instanton numbers in general gauge theories are also discussed.