映射环面与友矩阵的秩
Rank of mapping tori and companion matrices
摘要：
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判定的;如果是，可以将生成对分类到Nielsen等价.如果$f$具有无穷阶，则$f^n$的映射环面不能由足够大的$n$的两个元素生成;等价地，如果$n$大，则$f^n$不与$GL(d,Z)$中的友矩阵共轭。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
