Topological recursive relations in $H^{2g}(M_{g,n})$

Abstract

We show that any degree at least $g$ polynomial in descendant or tautological classes vanishes on $M_{g,n}$ when $g\ge 2$. This generalizes a result of Looijenga and proves a version of Getzler's conjecture. The method we use is the study of the relative Gromov-Witten invariants of $P^1$ relative 2 points combined with the degeneration formulas of [IP1]. At the end of the paper, we also included a quick proof of a very recent conjecture made by Vakil.

AMS-LaTeX, 27 pages, improved exposition

References in corpus (5)

• On the tautological ring of $\M _g$
• Virasoro constraints and the Chern classes of the Hodge bundle
• The Symplectic Sum Formula for Gromov-Witten Invariants
• Compactifying the space of stable maps
• Relative Gromov-Witten Invariants

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• Dynamical degrees of Hurwitz correspondences
• On the cohomological dimension of the moduli space of Riemann surfaces
• Combinatorics of binomial decompositions of the simplest Hodge integrals
• Intersections in genus 3 and the Boussinesq hierarchy