The Symplectic Geometry of Polygons in
Euclidean Space
Michael Kap ovich and John J Millson
March
Abstract
We study the symplectic geometry of mo duli spaces M of p oly
r
gons with xed side lengths in Euclidean space We show that M
r
has a natural structure of a complex analytic space and is complex
2 n
analytically isomorphic to the weighted quotient of S constructed
by Deligne and Mostow We study the Hamiltonian ows on M ob
r
tained by b ending the p olygon along diagonals and show the group
generated by such ows acts transitively on M We also relate these
r