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Point masses moving in 2+1 dimensions draw out braids in space-time. If they move under the influence of some pairwise potential, what braid types are possible? By starting with fictional paths of the desired topology and ``relaxing'' them by minimizing the action, we explore the braid types of potentials of the form Vr^ from -2, where all braid types occur, to =2, where the system is integrable. We also discuss issues of symmetry and stability. We propose this kind of topological classification as a tool for extending the ``symbolic dynamics'' approach to many-body dynamics.
Cristopher Moore (Mon,) studied this question.