Atiyah–Hitchin–Singer theorem

In differential geometry, the Atiyah–Hitchin–Singer theorem, introduced by Atiyah, Hitchin, and 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.

References

• Atiyah, Michael Francis; Hitchin, N. J.; Singer, I. M. (1977), "Deformations of instantons", Proceedings of the National Academy of Sciences of the United States of America 74 (7): 2662–2663, doi:10.1073/pnas.74.7.2662, ISSN 0027-8424, MR 0458424
• Atiyah, Michael Francis; Hitchin, N. J.; Singer, I. M. (1978), "Self-duality in four-dimensional Riemannian geometry", Proceedings of the Royal Society A 362 (1711): 425–461, doi:10.1098/rspa.1978.0143, ISSN 0080-4630, MR 506229