Gravity in 2 + 1 dimensions as a Riemann - Hilbert problem

In this paper we consider 2+1-dimensional gravity coupled to N point-particles. We introduce a gauge in which the z-and ¯ z-components of the dreibein field become holomorphic and anti-holomorphic respectively. As a result we can restrict ourselves to the complex plane. Next we show that solving the dreibein-field: e a z (z) is equivalent to solving the Riemann-Hilbert problem for the group SO(2, 1). We give the explicit solution for 2 particles in terms of hypergeometric functions. In the N-particle case we give a representation in terms of conformal field theory. The dreibeins are expressed as correlators of 2 free fermion fields and twistoperators at the position of the particles.