Hopf Algebras and Topological Recursion

TL;DR

This paper presents a Hopf algebraic model for topological recursion, extending a known algebra of trees to include loops, thereby deriving the Eynard-Orantin recursion formula.

Contribution

It introduces a novel Hopf algebra extension that captures the full topological recursion including loop graphs.

Findings

Derivation of the Eynard-Orantin recursion from algebraic structures

Extension of planar binary trees to graphs with loops

Unified algebraic framework for topological recursion

Abstract

We consider a model for topological recursion based on the Hopf Algebra of planar binary trees of Loday and Ronco. We show that extending this Hopf Algebra by identifying pairs of nearest neighbor leaves and producing in this way graphs with loops we obtain the full recursion formula of Eynard and Orantin.