Rotation index, Milnor--Munkres--Novikov pairing, and group actions on manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909899920769024 |
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| author | Bustamante, Mauricio Tshishiku, Bena |
| author_facet | Bustamante, Mauricio Tshishiku, Bena |
| contents | We introduce an invariant of a pair of commuting invertible matrices that we call the rotation index. We apply this invariant, together with the Milnor--Munkres--Novikov pairing, to the study of some questions about group actions of $\mathbb{Z}^2$, specifically the Nielsen realization problem, higher-rank Anosov actions, and extending actions from the sphere $S^{d-1}$ to the disk $D^d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09346 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rotation index, Milnor--Munkres--Novikov pairing, and group actions on manifolds Bustamante, Mauricio Tshishiku, Bena Geometric Topology Dynamical Systems 57S25 (primary), 57R60, 22E40, 37D20 (secondary) We introduce an invariant of a pair of commuting invertible matrices that we call the rotation index. We apply this invariant, together with the Milnor--Munkres--Novikov pairing, to the study of some questions about group actions of $\mathbb{Z}^2$, specifically the Nielsen realization problem, higher-rank Anosov actions, and extending actions from the sphere $S^{d-1}$ to the disk $D^d$. |
| title | Rotation index, Milnor--Munkres--Novikov pairing, and group actions on manifolds |
| topic | Geometric Topology Dynamical Systems 57S25 (primary), 57R60, 22E40, 37D20 (secondary) |
| url | https://arxiv.org/abs/2408.09346 |