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Local density of diffeomorphisms with large centralizers. (English) Zbl 1163.58003
Authors’ abstract: Given any compact manifold $$M$$, we construct a non-empty open subset $$\mathcal O$$ of the space Diff$$^1(M )$$ of $$C^1$$-diffeomorphisms and a dense subset $$\mathcal D \subset \mathcal O$$ such that the centralizer of every diffeomorphism in $$\mathcal D$$ is uncountable, hence non-trivial.

##### MSC:
 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds 57R05 Triangulating 57R50 Differential topological aspects of diffeomorphisms 58D99 Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
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