# Topological classification of Morse-Smale diffeomorphisms without heteroclinic curves on 3-manifolds

## TL;DR

This paper demonstrates that Morse-Smale diffeomorphisms without heteroclinic curves on 3-manifolds can be classified topologically using embeddings of stable and unstable laminations into a characteristic space, providing a complete classification scheme.

## Contribution

It introduces a topological classification method for Morse-Smale diffeomorphisms on 3-manifolds based on embeddings of heteroclinic laminations, extending understanding of their structure.

## Key findings

- Classification is complete up to topological conjugation.
- Embedding of laminations determines the diffeomorphism class.
- Provides a new framework for understanding Morse-Smale dynamics on 3-manifolds.

## Abstract

We show that, up to topological conjugation, the equivalence class of a Morse-Smale diffeomorphism without heteroclinic curves on 3-manifold is completely defined by an em- bedding of two-dimensional stable and unstable heteroclinic laminations to a characteristic space.