Topological Recursion Relations on ${\bar{\mathcal{M}}}_{3,2}$

Abstract

In this paper, we give some new genus-3 universal equations for Gromov-Witten invariants of compact symplectic manifolds. These equations were obtained by studying new relations in the tautological ring of the moduli space of 2-pointed genus-3 stable curves. A byproduct of our search for genus-3 equations is a new genus-2 universal equation for Gromov-Witten invariants.

48 pages, LaTex file

References in corpus (7)

• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Higher genus symplectic invariants and sigma model coupled with gravity
• Three questions in Gromov-Witten theory
• A Genus-3 Topological Recursion Relation
• Topological recursion relations and Gromov-Witten invariants in higher genus
• Cohomology of moduli spaces of curves of genus three via point counts
• The fourth tautological group of $\overline{{\mathcal{M}}_{g,n}}$ and relations with the cohomology