Computing top intersections in the tautological ring of ${mathcal{M}_g}$

摘要

We derive effective recursion formulae of top intersections in the tautological ring ${R^*(mathcal{M}_g)}$ of the moduli space of curves of genus g ≥ 2. As an application, we prove a convolution-type tautological relation in ${R^{g-2}(mathcal{M}_g)}$ and some interesting Bernoulli number identities.