ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

5. Differential Geometry and Global Analysis

1991 MS Classification: 53C15 Symington, Margaret, University of Texas at Austin, USA Symplectic rational blowdowns A rational blowdown is a surgery on a 4-manifold whose effect on Donaldson and Seiberg-Witten invariants can be computed. The surgery was developed by Fintushel and Stern. As one application, they used the rational blowdown to construct families of exotic 4-manifolds. They also showed that the exotic K3 surfaces of Gompf and Mrowka can be obtained by this surgery. All of the later manifolds and many of their own examples are shown to admit a symplectic structure by proving that the rational blowdown can be defined in the symplectic category. The proof exploits the toric structure of a neighborhood of the (symplectic) submanifolds along which the surgery occurs.