Rank of mapping tori and companion matrices
Rank of mapping tori and companion matrices
复制标题
映射环面矩阵和伴随矩阵的秩
DOI：
10.4171/lem/58-1-9
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
V. Metaftsis
中科院分区：
文献类型：
--
作者：
G. Levitt;V. Metaftsis
给定$GL(d，Z)$中的$f$，它的映射环面（$Z^d$与$Z$的半直积）是否可以由两个元素生成是可以确定的；如果是这样，就可以对生成对进行分类，直到尼尔森等价。如果$f$具有无限阶，则$f^n$的映射环面不能由两个元素生成，且$n$足够大；同样，如果$n$很大，$f^n$不共轭于$GL(d，Z)$中的伴矩阵。
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.