Polynomial recursion formula for linear Hodge integrals

Abstract

We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the Laplace transform of the cut-and-join equation for the simple Hurwitz numbers. We show that the recursion recovers the Witten-Kontsevich theorem when restricted to the top degree terms, and also the combinatorial factor of the lambda_g formula as the lowest degree terms.

References in corpus (9)

• A matrix model for simple Hurwitz numbers, and topological recursion
• Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models
• Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
• The equivariant Gromov-Witten theory of P^1
• Hodge integrals, Hurwitz numbers, and Symmetric Groups
• A simple proof of Witten conjecture through localization
• The Laplace transform of the cut-and-join equation and the Bouchard-Marino conjecture on Hurwitz numbers
• KP hierarchy for Hodge integrals
• A short proof of the lambda_g-conjecture without Gromov-Witten theory: Hurwitz theory and the moduli of curves

Cited by in corpus (2)

• Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formula
• Towards an orbifold generalization of Zvonkine's $r$-ELSV formula