Families of Morse functions for manifolds with boundary

TL;DR

This paper investigates the behavior of 1-parameter families of Morse functions on manifolds with boundary, identifying all possible degeneracies that can occur in generic cases.

Contribution

It provides a comprehensive classification of degeneracies in 1-parameter Morse function families on manifolds with boundary.

Findings

List of all possible degeneracies in generic families

Framework for analyzing Morse functions on manifolds with boundary

Insights into the structure of Morse function families

Abstract

We study 1-parameter families of Morse functions for manifolds with boundary. We list all degeneracies that may occur in generic 1-parameter families.