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Combinatorial classes on the moduli space of curves are tautological

Gabriele Mondello
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Abstract

The combinatorial description via ribbon graphs of the moduli space of Riemann surfaces makes it possible to define combinatorial cycles in a natural way. Witten and Kontsevich first conjectured that these classes are polynomials in the tautological classes. We answer affirmatively to this conjecture and find recursively all the polynomials.

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Gabriele Mondello. 2004-04-26. Combinatorial classes on the moduli space of curves are tautological. https://arxiv.org/abs/math/0303207

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