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arXiv · 0805.4829

New topological recursion relations

Xiaobo Liu·Rahul Pandharipande
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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.

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Xiaobo Liu, Rahul Pandharipande. 2010-04-22. New topological recursion relations. https://arxiv.org/abs/0805.4829

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