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Pré-Publication, Document De Travail Année : 2021

A natural basis for intersection numbers

Résumé

We advertise elementary symmetric polynomials $e_i$ as the natural basis for generating series $A_{g,n}$ of intersection numbers of genus g and n marked points. Closed formulae for $A_{g,n}$ are known for genera $0$ and $1$-- this approach provides formulae for $g = 2,3,4$, together with an algorithm to compute the formula for any g. The claimed naturality of the e_i basis relies in the unexpected vanishing of some coefficients with a clear pattern: we conjecture that $A_{g,n}$ can have at most $g$ factors $e_i$, with $i>1$, in its expansion. This observation promotes a paradigm for more general cohomology classes. As an application of the conjecture, we find new integral representations of $A_{g,n}$, which recover expressions for the Weil-Petersson volumes in terms of Bessel functions.

Dates et versions

hal-03321189 , version 1 (17-08-2021)

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Bertrand Eynard, Danilo Lewański, Adrien Ooms. A natural basis for intersection numbers. 2021. ⟨hal-03321189⟩
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