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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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