Some remarks concerning the rank of mapping tori and ascending HNN-extensions of abelian groups.

Francesco Amoroso (1) , Umberto Zannier (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 SNS - Scuola Normale Superiore di Pisa

Let A be a matrix in GL_d(Z) of infinite order. In a recent paper, G. Levitt and V. Metaftsis prove that for any sufficiently large n the matrix A^n is not conjugated to a companion matrix. We first prove a local version of this theorem. Then, we give an effective statement, using linear form in logarithms. We also discuss several related problems.

Mots clés: Mapping tori groups; diophantine approximation

Domaines: Théorie des nombres [math.NT]

Francesco Amoroso, Umberto Zannier. Some remarks concerning the rank of mapping tori and ascending HNN-extensions of abelian groups.. Rendiconti Lincei. Matematica e Applicazioni, 2012, 23 (2), pp.197-211. ⟨hal-00637093v2⟩