Orbit equivalence of Cantor minimal systems: A survey and a new proof

被引：8

作者：

Putnam, Ian F. ^{[1
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

来源：

EXPOSITIONES MATHEMATICAE | 2010年 / 28卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

ABSORPTION THEOREM; HOMEOMORPHISMS; DIMENSION; ALGEBRAS; SET;

D O I：

10.1016/j.exmath.2009.06.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a new proof of the classification, up to topological orbit equivalence, of minimal AF-equivalence relations and minimal actions of the group of integers on the Cantor set. This proof relies heavily on the structure of AF-equivalence relations and the theory of dimension groups; we give a short survey of these topics. (C) 2009 Elsevier GmbH. All rights reserved.

引用

页码：101 / 131

页数：31

共 6 条

[1] Orbit equivalence for Cantor minimal a"currency sign d -systems
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Matui, Hiroki
Putnam, Ian F.
Skau, Christian F.
INVENTIONES MATHEMATICAE, 2010, 179 (01) : 119 - 158
[2] Fundamental group of uniquely ergodic Cantor minimal systems
Nawata, Norio
ADVANCES IN MATHEMATICS, 2012, 230 (02) : 746 - 758
[3] COCYCLES FOR CANTOR MINIMAL Zd-SYSTEMS
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Skau, Christian F.
INTERNATIONAL JOURNAL OF MATHEMATICS, 2009, 20 (09) : 1107 - 1135
[4] Minimal dynamical systems on the product of the Cantor set and the circle II
Huaxin Lin
Hiroki Matui
Selecta Mathematica, 2006, 12
[5] Crossed product C*-algebras of minimal dynamical systems on the product of the Cantor set and the torus
Sun, Wei
JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (07) : 1105 - 1169
[6] A New Proof of the Gasca–Maeztu Conjecture for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\boldsymbol{n=5}$$\end{document}
G. Vardanyan
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2022, 57 (3): : 183 - 190

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