# University of Toronto's Symplectic Geometry Seminar

Sept. 15 2003, 2:10 - 3

SS5017A

## Megumi Harada

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University of Toronto

##
"Polygon and hyperpolygon spaces"

** 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.