Perfect Discrete Morse Functions on Connected Sums

TL;DR

This paper investigates the construction and decomposition of perfect discrete Morse functions on connected sums of closed oriented manifolds, providing methods to compose and decompose such functions across manifold sums.

Contribution

It introduces techniques for composing perfect discrete Morse functions on connected sums and decomposing them on surfaces, advancing understanding of Morse functions on complex manifolds.

Findings

Methods to compose perfect discrete Morse functions on connected sums.

Techniques for decomposing Morse functions on connected sums of surfaces.

Enhanced understanding of Morse functions in manifold topology.

Abstract

We study perfect discrete Morse functions on closed oriented n-dimensional manifolds. We show how to compose such functions on connected sums of closed oriented manifolds and how to decompose on connected sums of closed oriented surfaces.