# The indexed links of Non-singular Morse-Smale flows on graph manifolds

## TL;DR

This paper classifies the indexed links of non-singular Morse-Smale flows on graph manifolds, showing they can be generated from a fundamental link through finite operations, advancing understanding of flow topology.

## Contribution

It provides a classification method for indexed links of Morse-Smale flows on graph manifolds, identifying a finite set of operations to generate all such links.

## Key findings

- Indexed links can be obtained by finite operations on a fundamental link.
- The fundamental link includes all singular Seifert fibers and certain regular fibers.
- The classification applies to most graph manifolds.

## Abstract

We classify the indexed links corresponding to the union of the closed orbits of non-singular Morse-Smale flows on most graph manifolds. We find that each of this kind of indexed links can be obtained by applying a finite steps of operations on a special indexed link, which consists of all of the singular Seifert fibers and some regular Seifert fibers with some precisely described conditions.