  We construct a smooth family of Hamiltonian systems, together with a family
of group symmetries and momentum maps, for the dynamics of point vortices on
surfaces parametrized by the curvature of the surface. Equivariant bifurcations
in this family are characterized, whence the stability of the Thomson heptagon
is deduced without recourse to the Birkhoff normal form, which has hitherto
been a necessary tool.
