The closed chains with spherical configuration spaces

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_{...

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Bibliographic Details
Published in:Hiroshima mathematical journal 2012-07, Vol.42 (2), p.253-266
Main Authors: Goto, Satoru, Hemmi, Yutaka, Komatsu, Kazushi, Yagi, Jun
Format: Article
Language:English
Subjects:
52C99
57M50
58E05
92E10
Configuration space
molecular structure
Morse function
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Summary: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.
ISSN:0018-2079
DOI:10.32917/hmj/1345467073