D. Kotschick: Smooth Four-Manifolds

• Place and time: Tue+Thu 10-12 in B 041
• Exercise class: Thu 14-16 in B41
• Summary: We give a geometric introduction to smooth four-manifolds, discussing examples, the intersection form, the homotopy theory of four-manifolds, and embedded surfaces. We then develop the basics of Seiberg-Witten gauge theory on four-manifolds, and we apply this theory to the study of both topological and geometric properties of four-manifolds. The latter are related to the existence of complex and symplectic structures, and of special Riemannian metrics.
• Intended audience: Students of mathematics and/or physics.
• Prerequisites: Some knowledge of differential topology and geometry.
• Lecture notes: Lecture notes by the lecturer will be made available.
• Further references:
  S. K. Donaldson and P. B. Kronheimer: The Geometry of Four-Manifolds. Oxford University Press 1990.
  J. W. Morgan: The Seiberg-Witten equations and applications to the topology of smooth four-manifolds. Mathematical Notes, 44. Princeton University Press, Princeton, NJ, 1996.
  R. E. Gompf and A. I. Stipsicz: 4-Manifolds and Kirby Calculus, American Math. Soc. 1999.
• Exams: The course is worth 9 ECTS points. There will be oral exams at the end.