Morse flows with fixed points on the boundary of 3-manifold

TL;DR

This paper introduces a topological invariant called Pr-diagram for Morse flows with fixed points on the boundary of 3-manifolds, aiding in their classification and understanding.

Contribution

It develops a complete topological invariant, the Pr-diagram, specifically for Morse flows with boundary fixed points, extending tools for 3-manifold analysis.

Findings

Pr-diagram effectively classifies Morse flows with boundary fixed points.

The invariant parallels Heegaard diagrams for closed 3-manifolds.

Provides new insights into the structure of flows on 3-manifolds.

Abstract

The paper is devoted to the study of topological properties, structure and classification of Morse flows with fixed points on the boundary of three-dimensional manifolds. We construct a complete topological invariant of a Morse flow, Pr-diagram, which is similar to the Heegaard diagram of a closed 3-manifold.