The noncommutative topology of anti-self-dual gauge fields

Through techniques afforded by C*-algebras and Hilbert modules, we study the topology of spaces which parametrize families of instanton gauge fields on noncommutative Euclidean four-spheres S-sigma(4). By deforming the ADHM construction of instantons on the classical sphere S-4, we obtain families of instantons on the quantum sphere which are naturally parametrized by noncommutative topological spaces. Using the internal gauge theory of S-sigma(4) determined by the inner automorphisms of its function algebra, we find that one may always recover a classical parameter space by making a suitable choice of internal gauge. (C) 2013 Elsevier B.V. All rights reserved.