Abstract
AbstractLet Mn be the variety of spatial polygons P = (a1, a2, … ,an) whose sides are vectors ai ∈ R3 of length |ai| = 1 (1 ≤ i ≤ n), up to motion in R3. It is known that for odd n, Mn is a smooth manifold, while for even n, Mn has cone-like singular points. For odd n, the rational homology of Mn was determined by Kirwan and Klyachko [6], [9]. The purpose of this paper is to determine the rational homology of Mn for even n. For even n, let be the manifold obtained from Mn by the resolution of the singularities. Then we also determine the integral homology of .
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