The Poincaré dual of the Weil-Petersson Kähler two-form (Q1261730)

We consider a family of conjectures due to Witten which relate the Miller-Morita-Mumford cohomology classes to explicit cycles in a certain cell-decomposition of the moduli space of punctured Riemann surfaces. A version of the first of these conjectures is proved here, and the computational geometric proof leads directly to Rogers' version of the dilogarithm and its Abel-Spence functional equation.