Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I'm learning Yang-Mills theory and its applications on 4-manifold. I want to know that have someone computed all the anti-self-dual connections on principle $SU(2)$ bundles over complex projective space $CP^2$. Where can I find the original paper if someone has calculated it?

share|improve this question
Donaldson-Kronheimer's book The Geometry of Four-Manifolds computes the moduli space for small 2nd Chern class (it's empty for $c_2=1$); check the examples in chapter 4. But it's not computed by explicitly writing down connections (compared to the $S^4$ scenario). You should be able to find appropriate references there. –  Chris Gerig Jun 30 '13 at 18:26
You also have the Atiyah-Drinfeld-Hitchin-Manin construction en.wikipedia.org/wiki/ADHM_construction, on one side, and twistor space of Atiyah-Hitchin-Singer, or actually and originally R Penrose, on the other, which leads to complex algebraic geometry and results of Horrocks, Barth and Hartshorne. The twistor space of CP2 is the flag manifold F(C3)... –  Al-burcas Dec 16 '13 at 18:23
add comment

migrated from meta.mathoverflow.net Jun 30 '13 at 13:53

This question came from our discussion, support, and feature requests site for professional mathematicians.

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.