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# Symplectic Circle Actions

Friday, 14 April 2017 - 3:00pm

Dr. Susan Tolman, Univ. of Illinois - Urbana

LD 229

Let the circle act on a closed manifold M, preserving a symplectic form ω. We say that the action is Hamiltonian if there exists a moment map, that is, a map Ψ: M ® R such that ιc ω = -dΨ, where c is the vector field that generates the action. In this case, a great deal of information about the manifold is determined by the fixed set. Therefore, it is very important to determine when symplectic actions are Hamiltonian.

There has been a great deal of research on this question, but it left the following question, usually called the “McDuff conjecture”: Does there exists a non-Hamiltonian symplectic circle action with isolated fixed points on a closed, connected symplectic manifold? I will answer this question by constructing such an example

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