For any vector r = (r_1, . . . , r_n), let M_r denote the moduli space (under rigid motions) of polygons in ℝ^3 with n-sides whose lengths are r_1, . . . , r_n. We give an explicit characterization of the oriented S^1-cobordism class of M_r which depends uniquely on the length vector r.
The cobordism class of the moduli space of polygons in R3
Mandini, Alessia
2009-01-01
Abstract
For any vector r = (r_1, . . . , r_n), let M_r denote the moduli space (under rigid motions) of polygons in ℝ^3 with n-sides whose lengths are r_1, . . . , r_n. We give an explicit characterization of the oriented S^1-cobordism class of M_r which depends uniquely on the length vector r.
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[7] A. Mandini, The cobordism class of the moduli space of polygons in R3 , J. Symplectic Geom. 7, no. 1,?1–27, 2009.pdf
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