Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves

Details Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves

2010-09-11

arxiv.org/abs/1009.2135v2

Mathematics

Algebraic Geometry

16 pages, 5 figures

Scientific paper

We show that the Poincare polynomial associated with the orbifold cell decomposition of the moduli space of smooth algebraic curves with distinct marked points satisfies a topological recursion formula of the Eynard-Orantin type. The recursion uniquely determines the Poincare polynomials from the initial data. Our key discovery is that the Poincare polynomial is the Laplace transform of the number of Grothendieck's dessins d'enfants.

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