New topological recursion relations

Abstract

Simple boundary expressions for the k-th power of the cotangent line class on the moduli space of stable 1-pointed genus g curves are found for k >= 2g. The method is by virtual localization on the moduli space of maps to the projective line. As a consequence, nontrivial tautological classes in the kernel of the push-forward map associated to the irreducible boundary divisor of the moduli space of stable g+1 curves are constructed. The geometry of genus g+1 curves then provides universal equations in genus g Gromov-Witten theory. As an application, we prove all the Gromov-Witten identities conjectured recently by K. Liu and H. Xu.

13 pages. Corrected several typos in the first version. To appear in Journal of Algebraic Geometry.

References in corpus (3)

• The n-point functions for intersection numbers on moduli spaces of curves
• On Certain Vanishing Identities For Gromov-Witten Invariants
• Recursive formula for psi^g - lambda_1 psi^{g-1} + ... + (-1)^g lambda_g in \Mbar_{g,1}

Cited by in corpus (3)

• The n-point functions for intersection numbers on moduli spaces of curves
• Descendent integrals and tautological rings of moduli spaces of curves
• A proof of the Faber intersection number conjecture