Rohlin properties for ℤd actions on the cantor set

Michael Hochman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study the space H(d) of continuous ℤd-actions on the Cantor set, particularly questions related to density of isomorphism classes. For d = 1, Kechris and Rosendal showed that there is a residual conjugacy class. We show, in contrast, that for d ≥ 2 every conjugacy class in H(d) is meager, and that while there are actions with dense conjugacy class and the effective actions are dense, no effective action has dense conjugacy class. Thus, the action by the group homeomorphisms on the space of actions is topologically transitive but one cannot construct a transitive point. Finally, we show that in the spaces of transitive and minimal actions the effective action s are nowhere dense, and in particular there are minimal actions that are not approximable by minimal shifts of finite type.

Original languageAmerican English
Pages (from-to)1127-1143
Number of pages17
JournalTransactions of the American Mathematical Society
Issue number3
StatePublished - 2012


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