We give a geometric construction of the Harer complex for the Teichmuller space of a punctured surface. For a given finite area hyperbolic surface we construct a cut locus. The combinatorics of this cut locus determines the simplex of the Harer complex in which this surface lies as a point in Teichmuller space. The lengths of the projections of the edges of the cut locus onto a fixed set of horocycles determine the coordinates in this simplex. We explain how these coordinates can be extended over all of Teichmuller space, and show that the coordinate transformations are real analytic in a neighbourhood of each simplex, and hence give a real analytic atlas of Teichmuller space.
Topology 27 (1988) 91-117.