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 $S^{n-4}$.
Citation
Satoru Goto. Kazushi Komatsu. Jun Yagi. "The configuration space of almost regular polygons." Hiroshima Math. J. 50 (2) 185 - 197, July 2020. https://doi.org/10.32917/hmj/1595901626
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