Topological recursion, symplectic duality, and generalized fully simple maps

Abstract

For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions on the original curve. As a corollary, we prove topological recursion for the generalized fully simple maps generating functions.