Isometry transformations of hyperbolic 3-manifolds (Q1108615)
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scientific article; zbMATH DE number 4067877
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isometry transformations of hyperbolic 3-manifolds |
scientific article; zbMATH DE number 4067877 |
Statements
Isometry transformations of hyperbolic 3-manifolds (English)
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1988
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The author proves that every finite group is realizable as the full isometry group of some closed orientable hyperbolic 3-manifold. Corollary: any finite group occurs as \(\pi_ 0(Diff M)\) for some closed 3-manifold M. The constructions use Thurston's uniformization theorem and hyperbolic Dehn surgery theory.
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diffeomorphism groups of 3-manifolds
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finite group
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full isometry group of some closed orientable hyperbolic 3-manifold
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hyperbolic Dehn surgery
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