Classification of Special Anosov Endomorphisms of Nil-manifolds

In this paper we give a classification of special endomorphisms of nil-manifolds: Let f : N/Γ → N/Γ be a covering map of a nil-manifold and denote by A: N/Γ → N/Γ 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.