INTERSECTION-NUMBERS AND RANK-ONE COHOMOLOGICAL FIELD-THEORIES IN GENUS ONE

We obtain a simple recursive presentation of the tautological (kappa, psi, and lambda) classes on the moduli space of curves in genus 0 and 1 in terms of boundary strata (graphs). We derive differential equatio ns for the generating functions for their intersection numbers which a llow us to prove a simple relationship between the genus zero and genu s one potentials. As an application, we describe the moduli space of n ormalized, restricted, rank one cohomological field theories in genus one in coordinates which are additive under taking tensor products. Ou r results simplify and generalize those of Kaufmann, Manin, and Zagier .