Abstract
The structural stability in the sense of Adronov and Pontriagin is proved to be a property of any rearrangement occurring in a single electronic state sheet of the potential energy surface if such a rearrangement involves two internal degrees of freedom. It is then shown that features of no dynamical significance (the paths of steepest descent joining critical configurations) determine completely those of dynamical significance: The topology of the set of paths of steepest descent determines the triangulation of the nuclear configuration space which is rigorously derived from homology theory.
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