Rank of mapping tori and companion matrices

Details Rank of mapping tori and companion matrices Rank of mapping tori and companion matrices

2010-04-15

arxiv.org/abs/1004.2649v1

Mathematics

Group Theory

Scientific paper

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

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