In [GW], S. B. Giddings and S. A. Wolpert proposed a procedure to obtain a new cell decomposition of the moduli space of curves. In this paper, we work out this procedure in detail. The number of cells in this new cell decomposition is smaller than that in other cell decompositions given in [BE, Ha, P3] and this makes the explicit computations of the orbifold Euler numbers of the moduli spaces for small genera easier. We check in many examples that they coincide with the known value.
"A Calculation of the Orbifold Euler Number of the Moduli Space of Curves by a New Cell Decomposition of the Teichmüller Space." Tokyo J. Math. 23 (1) 87 - 100, June 2000. https://doi.org/10.3836/tjm/1255958809