A nonstandard construction of direct limit group actions

Manevitz and Weinberger proved that the existence of faithful $K$-Lipschitz $\mathbb{Z}/n\mathbb{Z}$-actions implies the existence of faithful $K$-Lipschitz $\mathbb{Q}/\mathbb{Z}$-actions. The $\mathbb{Q}/\mathbb{Z}$-actions were constructed from suitable actions of a sufficiently large hyperfinite cyclic group ${}^{\ast}\mathbb{Z}/\gamma{}^{\ast}\mathbb{Z}$ in the sense of nonstandard analysis. In this paper, we modify their construction, and prove that the existence of $\varepsilon$-faithful $K$-Lipschitz $G_{\lambda}$-actions implies the existence of $\varepsilon$-faithful $K$-Lipschitz $\varinjlim G_{\lambda}$-actions. In a similar way, we generalise Manevitz and Weinberger's result to injective direct limits of torsion groups

粗空間の超準的不変量

京都大学新制・課程博士博士(理学)甲第22978号理博第4655号新制||理||1669(附属図書館)京都大学大学院理学研究科数学・数理解析専攻(主査)准教授 照井 一成, 教授 長谷川 真人, 准教授 河村 彰星学位規則第4条第1項該当Doctor of ScienceKyoto UniversityDFA