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arXiv · 0907.5224

The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers

Bertrand Eynard·Motohico Mulase·Brad Safnuk
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Abstract

We calculate the Laplace transform of the cut-and-join equation of Goulden, Jackson and Vakil. The result is a polynomial equation that has the topological structure identical to the Mirzakhani recursion formula for the Weil-Petersson volume of the moduli space of bordered hyperbolic surfaces. We find that the direct image of this Laplace transformed equation via the inverse of the Lambert W-function is the topological recursion formula for Hurwitz numbers conjectured by Bouchard and Marino using topological string theory.

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Bertrand Eynard, Motohico Mulase, Brad Safnuk. 2009-07-29. The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers. https://arxiv.org/abs/0907.5224

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