Big polygon spaces

Big polygon spaces

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Matthias Franz, University of Western Ontario
Fine Hall 214

Big polygon spaces are compact orientable manifolds defined as the intersection of a product of spheres with a complex hyperplane given by a so-called length vector. They are related to polygon spaces, which appear as their fixed point set under a canonical torus action. What makes big polygon spaces interesting is that they exhibit remarkable new features in equivariant cohomology: The Chang-Skjelbred sequence can be exact for them and the equivariant Poincaré pairing perfect although these spaces fail to be equivariantly formal. We will in particular present a combinatorial formula that expresses the precise syzygy order of the equivariant cohomology of a big polygon space in terms of the length vector. This is in part joint work with Jianing Huang.