COMBINATORIAL CLASSES ON Mg,n ARE TAUTOLOGICAL

Abstract

Abstract. The combinatorial description via ribbon graphs of the moduli space of Riemann surfaces allows to define combinatorial cycles in a natural way. Witten and Kontsevich first conjectured that these classes are polynomials in the tautological classes. We answer affirmatively to this conjecture and find recursively all the polynomials. Moreover we lift the combinatorial classes to the Deligne-Mumford compactification of the moduli space and we give a partial answer to the same problem in this context.