2015/09/21 by Jessica Dyer, Dyer, Jessica, Steve Hurder +3 · 1 citation
Mathematics · #20F22 #37B10 (Secondary) #37B45 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #math.DS #math.GR #msc:20F22 #msc:37B10 #msc:37B45
paper · pdf · doi:10.48550/arxiv.1509.06227
27pp. The statement of Theorem 6.1 of the previous version was strengthened; it is now stated in Proposition 5.3 and Theorem 5.5. Sections of the paper were re-organized. To appear in Topology and Its Applications
arxiv created 2016/05/09 · arxiv updated 2016/05/10
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 1965 and Fokkink and Oversteegen 2002, 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.