Combinatorial and tautological classes on the moduli space of
curves
-- Gabriele Mondello, October 29, 2004

<p>

Every presentation of the moduli space of curves gives rise to
"natural" cohomology classes.
The so-called tautological classes appear in
the classical algebro-geometric setting. On the other side, the cellular
decomposition of the moduli space via the ribbon graph complex
makes it possible to define some interesting combinatorial cycles.
The aim of the talk is to discuss how to compare these two families of 
(co)homology classes.