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Stone-Čech boundaries of discrete groups and measure equivalence theory
https://doi.org/10.15083/00004022
https://doi.org/10.15083/000040221a8a55ad-acab-4b85-8125-2db6f4af1186
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SakoH_22_3_PhD_a.pdf (5.2 MB)
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SakoH_22_3_PhD_b.pdf (49.5 kB)
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Item type | 学位論文 / Thesis or Dissertation(1) | |||||
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公開日 | 2012-10-23 | |||||
タイトル | ||||||
タイトル | Stone-Čech boundaries of discrete groups and measure equivalence theory | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_46ec | |||||
タイプ | thesis | |||||
ID登録 | ||||||
ID登録 | 10.15083/00004022 | |||||
ID登録タイプ | JaLC | |||||
その他のタイトル | ||||||
その他のタイトル | 離散群のストーン-チェック境界と測度同値理論 | |||||
著者 |
SAKO, Hiroki
× SAKO, Hiroki |
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著者別名 | ||||||
識別子 | 9307 | |||||
識別子Scheme | WEKO | |||||
姓名 | 酒匂, 宏樹 | |||||
著者所属 | ||||||
著者所属 | 東京大学大学院数理科学研究科 | |||||
著者所属 | ||||||
著者所属 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
Abstract | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We get three types of results on measure equivalence theory: directproduct groups of Ozawa's class S groups, wreath product groups and amalgamatedfree products. We prove measure equivalence factorization results on directproduct groups of Ozawa's class S groups. As consequences, Monod-Shalom typeorbit equivalence rigidity theorems follow. We prove that if two wreath productgroups A≀G, B≀Γ of non-amenable exact direct product groups G, Γ with amenablebases A, B are measure equivalent, then G and Γ are measure equivalent. Rigidityresults on amalgamated free products of non-amenable exact direct productgroups are also shown. We also prove that being in Ozawa's class S of countablediscrete groups is invariant under measure equivalence. | |||||
書誌情報 | 発行日 2010-03-24 | |||||
日本十進分類法 | ||||||
主題 | 410 | |||||
主題Scheme | NDC | |||||
学位名 | ||||||
学位名 | 博士(数理科学) | |||||
学位 | ||||||
値 | doctoral | |||||
学位分野 | ||||||
Mathematical Sciences (数理科学) | ||||||
学位授与機関 | ||||||
学位授与機関名 | University of Tokyo (東京大学) | |||||
研究科・専攻 | ||||||
Graduate School of Mathematical Sciences (数理科学研究科) | ||||||
学位授与年月日 | ||||||
学位授与年月日 | 2010-03-24 | |||||
学位授与番号 | ||||||
学位授与番号 | 甲第26108号 | |||||
学位記番号 | ||||||
博数理第350号 |