## Hiroshima Mathematical Journal

### The closed chains with spherical configuration spaces

#### 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

#### 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