Hiroshima Mathematical Journal

The closed chains with spherical configuration spaces

Satoru Goto, Yutaka Hemmi, Kazushi Komatsu, and Jun Yagi

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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.

Article information

Source
Hiroshima Math. J., Volume 42, Number 2 (2012), 253-266.

Dates
First available in Project Euclid: 20 August 2012

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1345467073

Digital Object Identifier
doi:10.32917/hmj/1345467073

Mathematical Reviews number (MathSciNet)
MR2978305

Zentralblatt MATH identifier
1257.55012

Subjects
Primary: 52C99: None of the above, but in this section
Secondary: 57M50: Geometric structures on low-dimensional manifolds 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.) 92E10: Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

Keywords
Configuration space Morse function molecular structure

Citation

Goto, Satoru; Hemmi, Yutaka; Komatsu, Kazushi; Yagi, Jun. The closed chains with spherical configuration spaces. Hiroshima Math. J. 42 (2012), no. 2, 253--266. doi:10.32917/hmj/1345467073. https://projecteuclid.org/euclid.hmj/1345467073


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