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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.15004 |
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| _version_ | 1866912493110034432 |
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| author | Karshon, Yael Kuroki, Shintaro |
| author_facet | Karshon, Yael Kuroki, Shintaro |
| contents | An action of a torus T on a manifold M is locally standard if, at each point, the stabilizer is a sub-torus and the non-zero isotropy weights are a basis to its weight lattice. The quotient M/T is then a manifold-with-corners, decorated by a so-called unimodular labelling, which keeps track of the isotropy representations in M, and by a degree two cohomology class with coefficients in the integral lattice of the Lie algebra of T, which encodes the "twistedness" of M over M/T. We classify locally standard smooth actions of T, up to equivariant diffeomorphisms, in terms of triples (Q,lambda,c), where Q is a manifold-with-corners, lambda is a unimodular labelling, and c is a degree two cohomology class with coefficients in the integral lattice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15004 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of locally standard torus actions Karshon, Yael Kuroki, Shintaro Geometric Topology Symplectic Geometry 57S12, 57S25 An action of a torus T on a manifold M is locally standard if, at each point, the stabilizer is a sub-torus and the non-zero isotropy weights are a basis to its weight lattice. The quotient M/T is then a manifold-with-corners, decorated by a so-called unimodular labelling, which keeps track of the isotropy representations in M, and by a degree two cohomology class with coefficients in the integral lattice of the Lie algebra of T, which encodes the "twistedness" of M over M/T. We classify locally standard smooth actions of T, up to equivariant diffeomorphisms, in terms of triples (Q,lambda,c), where Q is a manifold-with-corners, lambda is a unimodular labelling, and c is a degree two cohomology class with coefficients in the integral lattice. |
| title | Classification of locally standard torus actions |
| topic | Geometric Topology Symplectic Geometry 57S12, 57S25 |
| url | https://arxiv.org/abs/2507.15004 |