12/4/2003
Michael Usher
MIT
The Gromov invariant and the Donaldson-Smith standard surface count
Abstract
I will discuss the equivalence of an invariant associated to four-dimensional symplectic Lefschetz fibrations that was introduced by Simon Donaldson and Ivan Smith to the Gromov invariant of Cliff Taubes which counts pseudoholomorphic submanifolds of symplectic 4-manifolds. As a consequence of this equivalence and of earlier work of Smith, there follows a new proof of a duality relation in the Gromov invariants (originally discovered by Taubes using Seiberg-Witten theory) that does not rely on gauge theory.