The configuration space of almost regular polygons

Abstract

For a given angle $\theta$, consider the configuration space $C_n$ of equilateral $n$-gons in $\mathbf R^3$ whose bond angles are equal to $\theta$ except for two successive ones. We show that when $n \ge 8$ and $\theta$ is sufficiently close to the inner angle $\frac{n-2}{n}\pi$ of the regular $n$-gon, $C_n$ is homeomorphic to the $(n-4)$-dimensional sphere $S^{n-4}$.