Hiroshima Mathematical Journal

The configuration space of a model for ringed hydrocarbon molecules

Satoru Goto and Kazushi Komatsu

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Abstract

We give a mathematical model of $n$-membered ringed hydrocarbon molecules, and study the topology of a configuration space $C_{n}$ of the model. Under the bond angle conditions required for ringed molecules, we prove that $C_{n}$ is homeomorphic to $(n-4)$-dimensional sphere $S^{n-4}$ when $n = 5, 6, 7$. This result gives an appropriate explanation of the configuration space of $n$-membered ringed hydrocarbon molecules when $n = 5, 6$.

Article information

Source
Hiroshima Math. J., Volume 42, Number 1 (2012), 115-126.

Dates
First available in Project Euclid: 30 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1333113009

Digital Object Identifier
doi:10.32917/hmj/1333113009

Mathematical Reviews number (MathSciNet)
MR2952075

Zentralblatt MATH identifier
1238.92069

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; Komatsu, Kazushi. The configuration space of a model for ringed hydrocarbon molecules. Hiroshima Math. J. 42 (2012), no. 1, 115--126. doi:10.32917/hmj/1333113009. https://projecteuclid.org/euclid.hmj/1333113009


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References

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