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.

References

• Atiyah, Michael F.; Hitchin, Nigel J.; Singer, Isadore 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, JSTOR 67216, MR 0458424, PMC 431234, PMID 16592414
• Atiyah, Michael F.; Hitchin, Nigel J.; Singer, Isadore 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 0506229