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Symplectic and Poisson geometry seminar: Lifting Complexity-1 Spaces to Toric Manifolds

Event Type
347 Altgeld Hall
Apr 25, 2022   3:00 pm  
Jason Liu
Joey Palmer

A toric manifold is a 2n dimensional compact connected symplectic manifold equipped with an n-dimensional torus acting effectively in a Hamiltonian manner. In 1980s, Delzant completely classified toric manifolds up to equivariant symplectomorphism by their moment images (Delzant polytopes). Given a toric manifold, we can take an (n-1)-dimensional subtorus and restrict our attention to the action of the subtorus. These spaces are important examples of complexity-1 space. A natural question to ask is: given a complexity-1 space, is there a way to lift it to a toric manifold? In this talk, I will first talk about complexity-1 spaces and present the explicit construction of lifting under certain assumptions. This is the joint work with Joey Palmer and Sue Tolman.

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