Abstract
On the torus of dimension 2, 3 or 4, we show that the subset of diffeomorphisms with trivial centralizer in the C1 topology has nonempty interior. We do this by developing two approaches, the fixed point and the odd prime periodic point, to obtain a trivial centralizer for an open neighbourhood of Anosov diffeomorphisms arbitrarily near certain irreducible hyperbolic toral automorphisms.
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