Topological bifurcations of central configurations in the NN-body problem

In this article we study topological bifurcations of classes of central configurations of the spatial 6- and 7-body problems. We treat these classes as SO(3)SO(3)-orbits of critical points of a family of SO(3)SO(3)-invariant potentials. Using the equivariant bifurcation theory technique, we prove the existence of a global topological bifurcation of classes of central configurations in the 7-body problem and a local topological bifurcation in the 6-body problem.