On connections by conjugation in dimension 1 and class \(C^1\) (Q2874608)
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scientific article; zbMATH DE number 6327853
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On connections by conjugation in dimension 1 and class \(C^1\) |
scientific article; zbMATH DE number 6327853 |
Statements
8 August 2014
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nilpotent group action
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action on the interval
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connectedness of spaces of diffeomorphisms
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0.8780856
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0.8744295
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0.8705287
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On connections by conjugation in dimension 1 and class \(C^1\) (English)
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The work concerns connectedness of some spaces of diffeomorphisms of the circle and of the interval.NEWLINENEWLINEThe author shows that the space of actions of every finitely generated nilpotent group by \(C^1\) orientation-preserving diffeomorphisms of the circle is path-connected. This is obtained via a general result which allows any given action of the interval to be connected to the trivial one by a continuous path of topological conjugates.NEWLINENEWLINEThe author addresses several open questions related to this result, concerning more general groups, and also concerning local connectedness.
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