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

Abstract

For any vector $r=(r_1,...,r_n)$, let $M_r$ denote the moduli space (under rigid motions) of polygons in ${\mathbb{R}}^3$ 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 $r$.

arXiv comment29 pages, 8 figures, Remark 9 added, circle action specified in main Theorem

References in corpus (1)

• Transversality theory, cobordisms, and invariants of symplectic quotients