, Volume 148, Issue 3, pp 627-658

Topological recursive relations in H2g(ℳg,n)

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We show that any degree at least g monomial in descendant or tautological classes vanishes on ℳ g,n when g≥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 ℙ1 relative to two points combined with the degeneration formulas of [IP1].