Unitary representations and differential representations of the group of diffeomorphisms and its applications (Q2751526)
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scientific article; zbMATH DE number 1664903
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unitary representations and differential representations of the group of diffeomorphisms and its applications |
scientific article; zbMATH DE number 1664903 |
Statements
30 April 2002
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unitary representation
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group of \(C^\infty\)-diffeomorphisms
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1-cocycles
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Unitary representations and differential representations of the group of diffeomorphisms and its applications (English)
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Let \(M\) be a compact Riemannian manifold and \((U,{\mathcal H})\) a unitary representation of the group of \(C^\infty\)-diffeomorphisms of \(M\) which are homotopic to the identity. Suppose that \((U,{\mathcal H})\) has a continuous extension to some group of \(C^k\)-diffeomorphisms homotopic to the identity. Then the set of \(C^\infty\)-vectors is dense in \(\mathcal H\). Some applications to \(1\)-cocycles are given.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00042].
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