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We present a full study of the 3-body problem in gravity in flat(2+1)-dimensional space-time, and in the nonrelativistic limit of smallvelocities. We provide an explicit form of the ADM Hamiltonian in a regularcoordinate system and we set up all the ingredients for canonical quantization.We emphasize the role of a U(2) symmetry under which the Hamiltonian isinvariant and which should generalize to a U(N-1) symmetry for N bodies. Thissymmetry seems to stem from a braid group structure in the operations oflooping of particles around each other, and guarantees the single-valuedness ofthe Hamiltonian. Its role for the construction of single-valued energyeigenfunctions is also discussed.

Hamiltonian solutions of the 3-body problem in (2+1)-gravity