A combinatorial construction of the moduli space of flowlines in discrete Morse theory

TL;DR

This paper constructs the moduli space of index 2 flowlines in discrete Morse theory, providing a new proof that the Morse differential squares to zero, thereby advancing understanding of discrete Morse homology.

Contribution

It introduces a combinatorial construction of the moduli space of flowlines, offering a novel proof of the differential's property in discrete Morse homology.

Findings

Established a combinatorial model for the moduli space of flowlines.

Provided a new proof that the Morse differential squares to zero.

Enhanced the theoretical framework of discrete Morse homology.

Abstract

We construct the moduli space of index 2 flowlines of a discrete Morse function, giving a new proof that the Morse differential squares to zero in discrete Morse homology.