April 16, 2007

Liat Kessler (MIT):   A compact symplectic four-manifold admits only finitely many toric actions: soft and hard proofs.

Abstract:

Let (M,\omega) be a four dimensional compact connected symplectic manifold. We prove that (M,\omega) admits only finitely many inequivalent Hamiltonian effective 2-torus actions. Consequently, if M is simply connected, the number of conjugacy classes of 2-tori in the symplectomorphism group is finite. We give two proofs: one using ``soft'' equivariant, algebraic, and combinatorial techniques, and another using ``hard'' J-holomorphic techniques. This is a joint work with Yael Karshon and Martin Pinsonnault.

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