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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