On framed simple purely real Hurwitz numbers

TL;DR

This paper investigates a specific class of real Hurwitz numbers associated with simple framed purely real functions, deriving differential equations and constructing a topological field theory to understand their properties.

Contribution

It introduces the concept of simple framed purely real functions and develops new differential equations and a topological field theory for their enumeration.

Findings

Derived cut-and-join type PDEs for generating functions.

Constructed a topological field theory for these real Hurwitz numbers.

Provided new insights into the structure of real meromorphic functions.

Abstract

We present a study of real Hurwitz numbers enumerating a special kind of real meromorphic functions, which we call simple framed purely real functions. We deduce partial differential equations of cut-and-join type for generating functions for these numbers. We also construct a topological field theory for them.