Mathematical Research Letters

Volume 23 (2016)

Number 5

Orbifold Hurwitz numbers and Eynard–Orantin invariants

Pages: 1281 – 1327

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n5.a3

Authors

Norman Do (School of Mathematical Sciences, Monash University, Clayton, Victoria, Australia)

Oliver Leigh (Department of Mathematics and Statistics, University of Melbourne, Victoria, Australia)

Paul Norbury (Department of Mathematics and Statistics, University of Melbourne, Victoria, Australia)

Abstract

We prove that a generalisation of simple Hurwitz numbers due to Johnson, Pandharipande and Tseng satisfies the topological recursion of Eynard and Orantin. This generalises the Bouchard–Mariño 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.

2010 Mathematics Subject Classification

05A15, 14N35, 32G15

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Published 12 January 2017