A remark on the configuration space of a model for ringed hydrocarbon molecules (Q2906877)

The authors construct a configuration space model \(C_{n}\) for an \(n\)-membered ring of hydrocarbon molecules. This space takes into account the vertices, bonds and the bond angle. The authors show that for \(n\) equal to \(5,6\), and \(7\) the configuration space \(C_{n}\) is diffeomorphic to the \((n-4)\)-sphere. The methods rely on finding a Morse function that has just two critical points.