Rank of mapping tori and companion matrices
Rank of mapping tori and companion matrices
Given an element \varphi\in \mathrm {GL}(d,\mathbb Z) , consider the mapping torus defined as the semidirect product G=\mathbb Z^d\rtimes_\varphi\mathbb Z . We show that one can decide whether G has rank 2 or not (i.e.\ whether G may be generated by two elements). When G is 2-generated, one may classify …