2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76447In Part 1 of this paper, we study gravitational descendents of Gromov-Witten invariants for general projective manifolds, applying the Behrend-Fantechi construction of the virtual fundamental classes. In Part 2, we calculate the topological recursion relations in genus 2. There are two of these, one for the second descendent of a field, and one for the first descendents of two fields. The proof uses the results of Part 1 together with a thorough study of intersection theory on the moduli space $\bar{M}_{2,2}$.28 pages, AMS-LaTeX 1.2 (with lamsarrow)Algebraic GeometryHigh Energy Physics - Theory14H10 (Primary) 81T40 (Secondary)text