A new cohomology class on the moduli space of curves

Abstract

We define a collection 0g,ne H4g~4+2n(Mg,n, Q) for 2g - 2 + n > 0 of cohomology classes that restrict naturally to boundary divisors. We prove that the intersection numbersn®g,nEHD ^T1can be recursively calculated. We conjecture that a generating function for these intersection numbers is a tau function of the KdV hierarchy. This is analogous to the conjecture of Witten proven by Kontsevich that a generating function for the intersection numbers f^gnEl'n=1ir’Tlis a tau function of the KdV hierarchy.