The discriminant invariant of Cantor group actions

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• 作者：Jessica Dyer ^{jesscdyer@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Steven Hurder ^{hurder@uic.edu" class="auth_mail" title="E-mail the corresponding author} ; Olga Lukina ; ^{lukina@math.uic.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 37B45 ; secondary ; 20F22 ; 37B10
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 August 2016
• 年：2016
• 卷：208
• 期：Complete
• 页码：64-92
• 全文大小：656 K

文摘

In this work, we investigate the dynamical and geometric properties of weak solenoids, as part of the development of a “calculus of group chains” associated to Cantor minimal actions. The study of the properties of group chains was initiated in the works of McCord [23] and Fokkink and Oversteegen [14], to study the problem of determining which weak solenoids are homogeneous continua. We develop an alternative condition for the homogeneity in terms of the Ellis semigroup of the action, then investigate the relationship between non-homogeneity of a weak solenoid and its discriminant invariant, which we introduce in this work. A key part of our study is the construction of new examples that illustrate various subtle properties of group chains that correspond to geometric properties of non-homogeneous weak solenoids.