Actions on positively curved manifolds and boundary in the orbit space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866914688313327616 |
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| author | Gorodski, Claudio Kollross, Andreas Wilking, Burkhard |
| author_facet | Gorodski, Claudio Kollross, Andreas Wilking, Burkhard |
| contents | We study isometric actions of compact Lie groups on complete orientable positively curved $n$-manifolds whose orbit spaces have non-empty boundary in the sense of Alexandrov geometry. In particular, we classify quotients of the unit sphere by actions of compact simple Lie groups with non-empty boundary. We deduce from this the list of representations of compact simple Lie groups that admit non-trivial reductions. As a tool of special interest, we introduce a new geometric invariant of a compact symmetric space, namely, the minimal number of points in a "spanning set" of the space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_00513 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Actions on positively curved manifolds and boundary in the orbit space Gorodski, Claudio Kollross, Andreas Wilking, Burkhard Differential Geometry Representation Theory 57S15 53C21 53C35 We study isometric actions of compact Lie groups on complete orientable positively curved $n$-manifolds whose orbit spaces have non-empty boundary in the sense of Alexandrov geometry. In particular, we classify quotients of the unit sphere by actions of compact simple Lie groups with non-empty boundary. We deduce from this the list of representations of compact simple Lie groups that admit non-trivial reductions. As a tool of special interest, we introduce a new geometric invariant of a compact symmetric space, namely, the minimal number of points in a "spanning set" of the space. |
| title | Actions on positively curved manifolds and boundary in the orbit space |
| topic | Differential Geometry Representation Theory 57S15 53C21 53C35 |
| url | https://arxiv.org/abs/2112.00513 |