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Monday, February 23, 2015

**Abstract:** Consider a symplectic circle action on a compact symplectic manifold with isolated fixed points. We can associate a directed multigraph to the manifold. Y. Karshon proved that if the dimension of the manifold is four, this multigraph completely determines the manifold up to equivariant symplectomorphism. We prove that we can associate a multigraph that does not have any loops. As an application, we complete the proof of the symplectic Petrie's conjecture for eight dimensional manifolds. This is a joint work with S. Tolman. arXiv:1408.6580.