# Pairs of Morse functions

## TL;DR

This paper classifies pairs of Morse functions in general position under various group actions, providing a comprehensive framework for understanding their equivalence and conjugation properties.

## Contribution

It introduces a classification scheme for generic pairs of Morse functions, including quotients, and presents a lemma for conjugation conditions.

## Key findings

- Classification of generic pairs of Morse functions with target diffeomorphisms
- Classification of quotients of Morse functions
- A lemma for conjugation of pairs of functions

## Abstract

The goal of this paper is to classify pairs of Morse functions in general position modulo the action of different groups.In particular, we obtain the classification of generic pairs of Morse functions, with or without target diffeomorphisms, and that of quotients of Morse functions.We will also present a lemma which gives a sufficient condition for two pairs of functions to be conjugated.