Discrete Morse-Bott theory for CW complexes

TL;DR

This paper develops a discrete Morse-Bott theory for CW complexes, extending Forman's discrete Morse theory, and applies it to Conley theory analysis for topological spaces.

Contribution

It introduces a novel discrete Morse-Bott framework that generalizes existing discrete Morse theory for CW complexes.

Findings

Discrete Morse-Bott theory generalizes Forman's discrete Morse theory.

Application to Conley theory provides new analytical tools.

Framework enhances topological analysis of CW complexes.

Abstract

We derive a discrete analogue of Morse-Bott theory on CW complexes and use this discrete Morse-Bott function to do some Conley theory analysis. It turns out that our discrete Morse-Bott theory is indeed a generalization of Forman's discrete Morse theory.