JournalsrlmVol. 23, No. 2pp. 197–211

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

  • Francesco Amoroso

    Université de Caen, France
  • Umberto Zannier

    Scuola Normale Superiore, Pisa, Italy
Some remarks concerning the rank of mapping tori and ascending HNN-extensions of abelian groups cover

Abstract

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

Cite this article

Francesco Amoroso, Umberto Zannier, Some remarks concerning the rank of mapping tori and ascending HNN-extensions of abelian groups. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 23 (2012), no. 2, pp. 197–211

DOI 10.4171/RLM/624