On the Moduli Space of Polygons in the Euclidean Plane
نویسندگان
چکیده
We study the topology of moduli spaces of polygons with xed side lengths in the Euclidean plane. We establish a duality between the spaces of marked Euclidean polygons with xed side lengths and marked convex Euclidean polygons with prescribed angles. 1. We consider the space P n of all polygons with n distinguished vertices in the Euclidean plane E 2 whose sides have nonnegative length allowing all possible degenerations of the polygons except of the degeneration of the polygon to a point. Two polygons are identiied if there exists an orientation preserving similarity of the complex plane C = E 2 which sends vertices of one polygon to vertices of another one. We shall denote the edges of the n-gon P by: e 1
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