University of Toronto's Symplectic Geometry Seminar

Abstract: Polygon spaces are moduli spaces of polygons in ${\mathbb R}^3$ with fixed sidelengths. They can also be realized as GIT/Kahler/symplectic quotients of affine space, and in particular are examples of Kahler quiver varieties. The hyperKahler versions of polygon spaces, the hyperpolygon spaces, have a residual $S^1$-action which is our principal tool for understanding their topology. In this talk, I will recall some of the geometrical considerations involved in calculating the cohomology of the Kahler polygon spaces (Hausman-Knutson), and then give an explicit, similarly polygon-theoretical calculation of the $S^1$-equivariant cohomology rings of the hyperpolygon spaces. This is joint work with Nicholas Proudfoot.