Teichmuller geometry of moduli space, II: M(S) seen from far away

We construct a metric simplicial complex which is an almost isometric model of the moduli space M(S) of Riemann surfaces. We then use this model to compute the “tangent cone at infinity” of M(S): it is the topological cone on the quotient of the complex of curves C(S) by the mapping class group of S, endowed with an explicitly described metric. The main ingredient is Minsky’s product regions theorem.