A proof of Morse's theorem about the cancellation of critical points

TL;DR

This paper provides a simplified proof of Morse's theorem on canceling pairs of non-degenerate critical points by reducing the problem to a one-dimensional case, making the proof more accessible.

Contribution

It introduces a new, simplified proof of Morse's theorem by reducing the problem to a one-dimensional scenario, enhancing understanding.

Findings

Proof reduces the problem to one dimension for simplicity

Clarifies the process of canceling critical points

Provides an accessible proof of Morse's theorem

Abstract

In this note, we give a proof of the famous theorem of M. Morse dealing with the cancellation of a pair of non-degenerate critical points of a smooth function. Our proof consists of a reduction to the one-dimensional case where the question becomes easy to answer.