Atiyah–Hitchin–Singer theorem

In differential geometry and gauge theory, the Atiyah–Hitchin–Singer theorem, introduced by Michael Atiyah, Nigel Hitchin, and Isadore Singer (1977, 1978), states that the space of SU(2) anti self dual Yang–Mills fields on a 4-sphere with index k > 0 has dimension 8k – 3.