Étale groupoids arising from products of shifts of finite type

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• 作者：Hiroki Matui¹ ; ^{matui@math.s.chiba-u.ac.jp" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Etale groupoids ; Shifts of finite type ; Topological full groups ; Higman&ndash ; Thompson groups
• 刊名：Advances in Mathematics
• 出版年：2016
• 出版时间：5 November 2016
• 年：2016
• 卷：303
• 期：Complete
• 页码：502-548
• 全文大小：702 K

文摘

Two conjectures about homology groups, K-groups and topological full groups of minimal étale groupoids on Cantor sets are formulated. We verify these conjectures for many examples of étale groupoids including products of étale groupoids arising from one-sided shifts of finite type. Furthermore, we completely determine when these product groupoids are mutually isomorphic. Also, the abelianization of their topological full groups is computed. They are viewed as generalizations of the higher dimensional Thompson groups.