# A note on collapsibility of acyclic 2-complexes

## TL;DR

This paper introduces a Morse-theoretic approach to determine when 2-dimensional acyclic simplicial complexes can be collapsed, using optimized combinatorial Morse functions to characterize collapsibility.

## Contribution

It provides a novel Morse-theoretic characterization of collapsibility for acyclic 2-complexes based on normalized optimal Morse functions.

## Key findings

- Morse-theoretic criteria for collapsibility
- Use of normalized optimal combinatorial Morse functions
- Characterization applicable to 2-dimensional acyclic complexes

## Abstract

We present a Morse-theoretic characterization of collapsibility for 2-dimensional acyclic simplicial complexes by means of the values of normalized optimal combinatorial Morse functions.