An irregular spectral curve for the generation of bipartite maps in topological recursion

  • Johannes Branahl

    Universität Münster, Münster, Germany
  • Alexander Hock

    University of Oxford, Oxford, UK
An irregular spectral curve for the generation of bipartite maps in topological recursion cover

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Abstract

We derive an efficient way to obtain generating functions of bipartite maps of arbitrary genus and boundary length using a spectral curve as initial data for the framework of topological recursion. Based on an earlier result of Chapuy and Fang counting these maps and having a structural proximity to topological recursion, we deduce the corresponding spectral curve which has a strong relation to the spectral curve giving rise to generating functions of ordinary maps. In contrast to ordinary maps, the spectral curve is an irregular one in the sense of Do and Norbury. It generalises the irregular curve for the enumeration of Grothendieck’s dessins d’enfant.

Cite this article

Johannes Branahl, Alexander Hock, An irregular spectral curve for the generation of bipartite maps in topological recursion. Ann. Inst. Henri Poincaré Comb. Phys. Interact. (2024), published online first

DOI 10.4171/AIHPD/190