The cobordism class of the moduli space of polygons in \(\mathbb{R}^3\) (Q1026949)

Given any \(n\)-tuple of positive numbers \(r=(r_1,\dots,r_n)\), let us denote by \(M_r\) space of the polygons with \(n\) vertices in the 3-dimensional Euclidean space with the lengths of the edges equal to \(r_1,\dots,r_n\), respectively, modulo the group of orientation preserving isometries. The main theorem of the paper under review provides an explicit description for the oriented \(S^1\)-cobordism class of the moduli space \(M_r\). The special case \(n=5\) is then carefully analyzed and specific examples are indicated for each cobordism type.