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July 2012 The closed chains with spherical configuration spaces
Satoru Goto, Yutaka Hemmi, Kazushi Komatsu, Jun Yagi
Hiroshima Math. J. 42(2): 253-266 (July 2012). DOI: 10.32917/hmj/1345467073

Abstract

As a mathematical model of $n$-membered ringed hydrocarbon molecules, we consider closed chains in $\R^{3}$. Assume that the bond angle $\theta$ satisfies $\frac{n-4}{n-2}\pi0\theta0\frac{n-2}{n}\pi$ when $n=5,6,7$, and that $\frac{5}{7}\pi \leq \theta0 \frac{3}{4}\pi$ when $n=8$. Then the configuration space $C_{n}$ of the model is homeomorphic to $(n-4)$-dimensional sphere $S^{n-4}$. By this result, it is possible for approximating larger macrocyclic molecules by smaller ones to be more widely applied.

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Satoru Goto. Yutaka Hemmi. Kazushi Komatsu. Jun Yagi. "The closed chains with spherical configuration spaces." Hiroshima Math. J. 42 (2) 253 - 266, July 2012. https://doi.org/10.32917/hmj/1345467073

Information

Published: July 2012
First available in Project Euclid: 20 August 2012

zbMATH: 1257.55012
MathSciNet: MR2978305
Digital Object Identifier: 10.32917/hmj/1345467073

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

Rights: Copyright © 2012 Hiroshima University, Mathematics Program

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Vol.42 • No. 2 • July 2012
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