Rank of mapping tori and companion matrices
Gilbert Levitt
Université de Caen Basse-Normandie, Caen, FranceVassilis Metaftsis
University of the Aegean, Karlovassi, Greece
Abstract
Given an element , consider the mapping torus defined as the semidirect product . We show that one can decide whether has rank or not (i.e.\ whether may be generated by two elements). When is 2-generated, one may classify generating pairs up to Nielsen equivalence. If has infinite order, we show that the rank of is at least 3 for all large enough; equivalently, is not conjugate to a companion matrix in GL if is large.
Cite this article
Gilbert Levitt, Vassilis Metaftsis, Rank of mapping tori and companion matrices. Enseign. Math. 58 (2012), no. 1, pp. 189–203
DOI 10.4171/LEM/58-1-9