University of Toronto's Symplectic Geometry Seminar

Abstract: I will present a classification of symplectic actions of 2-tori on compact, connected symplectic 4-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg and Delzant and Benoist. Our classification is in terms of a collection of invariants of the topology of the manifold, of the torus action and of the symplectic form. I will construct explicit models of such symplectic manifolds with torus actions, defined in terms of these invariants. (Some results are joint with JJ Duistermaat. This is part of my PhD thesis, supervised by Y Karshon).