Topological recursion relations in genus 2

Abstract

In 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)

References in corpus (3)

• Higher genus symplectic invariants and sigma model coupled with gravity
• Quantum Cohomology and Virasoro Algebra
• Relations between the correlators of the topological sigma-model coupled to gravity

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