Donaldson theory
From Wikipedia, the free encyclopedia
Donaldson theory is the study of smooth 4-manifolds using gauge theory. It was started by Donaldson (1983) who proved Donaldson's theorem restricting the possible quadratic forms on the second cohomology group of a compact simply connected 4-manifold.
Most of the results of Donaldson theory depend on the manifold having a differential structure, and are false for topological 4-manifolds.
Many of the theorems in Donaldson theory can now be proved more easily using Seiberg-Witten theory.
[edit] References
- Donaldson, Simon. An Application of Gauge Theory to Four Dimensional Topology. Journal of Differential Geometry vol. 18, 1983, 279-315.
- S. K. Donaldson, P. B. Kronheimer The Geometry of Four-Manifolds (Oxford Mathematical Monographs) ISBN 0-19-850269-9
- D.S. Freed, K.K. Uhlenbeck, Instantons and four-manifolds , Springer (1984)
- A. Scorpan, The wild world of 4-manifolds, ISBN 0-8218-3749-4
