Virtual Euler characteristics via topological recursion

Abstract

We use Seiberg--Witten-like relations in the topological recursion framework to obtain virtual Euler characteristics for uni- and multicellular maps for ensembles of classic orthogonal polynomials and for ensembles related to nonorientable surfaces. We also discuss Harer--Zagier-type recursion relations for 1-point correlation function for the Legendre ensemble.

13 pages, 1 figure, version 2 with extensive revision. Version 3: added description of moduli spaces of nonoriented surfaces