The configuration space of a model for ringed hydrocarbon molecules

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 $n = 5, 6$.