English

Rank of mapping tori and companion matrices

Group Theory 2019-06-07 v1

Abstract

Given ff in GL(d,Z)GL(d,Z), it is decidable whether its mapping torus (the semi-direct product of ZdZ^d with ZZ) may be generated by two elements or not; if so, one can classify generating pairs up to Nielsen equivalence. If ff has infinite order, the mapping torus of fnf^n cannot be generated by two elements for nn large enough; equivalently, fnf^n is not conjugate to a companion matrix in GL(d,Z)GL(d,Z) if nn is large.

Keywords

Cite

@article{arxiv.1004.2649,
  title  = {Rank of mapping tori and companion matrices},
  author = {Gilbert Levitt and Vassilis Metaftsis},
  journal= {arXiv preprint arXiv:1004.2649},
  year   = {2019}
}