“…However, determining the braid types of the solutions (other than relative equilibria) obtained in Theorem 2.2 is a non-trivial task. For most choices of masses in the three-body problem, existence of solutions in H φ,T,R,B −1 (that is, the space of retrograde paths in H φ,T,R ) with φ away from zero was proved in [4] (see also [5]). We conjecture that, for any n, the action-minimizing solutions obtained in Theorem 2.2 for φ ∈ (φ c , π] have non-trivial braid types.…”