# Classification of special Anosov endomorphisms of nil-manifolds

## TL;DR

This paper classifies special endomorphisms of nil-manifolds, showing that such maps are topologically conjugate to hyperbolic nil-endomorphisms when they are special TA-maps.

## Contribution

It provides a classification result for special endomorphisms of nil-manifolds, linking them to hyperbolic nil-endomorphisms via topological conjugacy.

## Key findings

- Special endomorphisms are conjugate to hyperbolic nil-endomorphisms.
- The classification applies to special TA-maps on nil-manifolds.
- Homotopic maps share conjugacy properties.

## Abstract

In this paper we give a classification of special endomorphisms of nil-manifolds: Let $f:N/\Gamma \rightarrow N/\Gamma$ be a covering map of a nil-manifold and denote by $A:N/\Gamma \rightarrow N/\Gamma$ the nil-endomorphism which is homotopic to $f$. If $f$ is a special $TA$-map, then $A$ is a hyperbolic nil-endomorphism and $f$ is topologically conjugate to $A$.