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July 2020 The configuration space of almost regular polygons
Satoru Goto, Kazushi Komatsu, Jun Yagi
Hiroshima Math. J. 50(2): 185-197 (July 2020). DOI: 10.32917/hmj/1595901626

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

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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

Information

Received: 5 July 2018; Revised: 3 February 2020; Published: July 2020
First available in Project Euclid: 28 July 2020

zbMATH: 07256503
MathSciNet: MR4132587
Digital Object Identifier: 10.32917/hmj/1595901626

Subjects:
Primary: 52C99
Secondary: 57M50, 58E05, 92E10

Rights: Copyright © 2020 Hiroshima University, Mathematics Program

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Vol.50 • No. 2 • July 2020
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