Aaron Hill
Published 2012-02-09Version 1
We give a definition for a rank-1 homeomorphism of a zero-dimensional Polish space X. We show that if a rank-1 homeomorphism of X satisfies a certain non-degeneracy condition, then it has trivial centralizer in the group of all homeomorphisms of X, i.e., it commutes only with its integral powers.
Trivial centralizers for Axiom A diffeomorphisms
Conjugacy class of homeomorphisms and distortion elements in groups of homeomorphisms
Open sets of diffeomorphisms with trivial centralizer in the $C^1$ topology
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