Orbifold Hurwitz numbers and Eynard-Orantin invariants

TL;DR

This paper demonstrates that a generalized form of Hurwitz numbers related to orbifold structures satisfies the Eynard-Orantin topological recursion, connecting Hurwitz-Hodge integrals to this recursive framework.

Contribution

It proves that orbifold Hurwitz numbers follow the Eynard-Orantin recursion, extending previous conjectures and linking Gromov-Witten theory with topological recursion.

Findings

Orbifold Hurwitz numbers satisfy topological recursion.

Generalizes Bouchard-Marino conjecture.

Connects Hurwitz-Hodge integrals to Eynard-Orantin invariants.

Abstract

We prove that a generalisation of simple Hurwitz numbers due to Johnson, Pandharipande and Tseng satisfy the topological recursion of Eynard and Orantin. This generalises the Bouchard-Marino conjecture and places Hurwitz-Hodge integrals, which arise in the Gromov--Witten theory of target curves with orbifold structure, in the context of the Eynard-Orantin topological recursion.