Actions of compact connected Lie groups on simply connected rational cohomology 5-spheres (Q1121564)
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scientific article; zbMATH DE number 4104013
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Actions of compact connected Lie groups on simply connected rational cohomology 5-spheres |
scientific article; zbMATH DE number 4104013 |
Statements
Actions of compact connected Lie groups on simply connected rational cohomology 5-spheres (English)
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1989
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Hudson classified simply connected closed 5-manifolds with SO(3)-actions admitting at least one singular orbit up to SO(3)-equivariant diffeomorphisms. Ōike classified simply connected closed 5-manifolds with effective U(2)-actions up to U(2)-equivariant diffeomorphisms. It is interesting to know what types of Lie groups other than SO(3) and U(2) can act smoothly and effectively on simply connected closed smooth 5- manifolds. In this note we shall particularly consider such actions on simply connected rational cohomology 5-spheres and classify compact connected non-commutative Lie groups other than SO(3) and U(2) acting smoothly and effectively on the spaces up to isomorphism.
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compact Lie groups which act on simply connected 5-manifolds
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smooth actions
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simply connected rational cohomology 5-spheres
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compact connected non-commutative Lie groups
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