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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.14553 |
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| _version_ | 1866909940672626688 |
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| author | Panina, Gaiane Shamazov, Timur Turevskii, Maksim |
| author_facet | Panina, Gaiane Shamazov, Timur Turevskii, Maksim |
| contents | The Milnor-Wood inequality states that if a (topological) oriented circle bundle over an orientable surface of genus $g$ has a smooth transverse foliation, then the Euler class of the bundle satisfies $$|\mathcal{E}|\leq 2g-2.$$ We give a new proof of the inequality based on a (previously proven by the authors) local formula which computes $\mathcal{E}$ from the singularities of a quasisection.
We also sketch two other proofs: one based on Poincarè rotation number theory, and the other of topological nature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14553 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A new proof of Milnor-Wood inequality Panina, Gaiane Shamazov, Timur Turevskii, Maksim Geometric Topology The Milnor-Wood inequality states that if a (topological) oriented circle bundle over an orientable surface of genus $g$ has a smooth transverse foliation, then the Euler class of the bundle satisfies $$|\mathcal{E}|\leq 2g-2.$$ We give a new proof of the inequality based on a (previously proven by the authors) local formula which computes $\mathcal{E}$ from the singularities of a quasisection. We also sketch two other proofs: one based on Poincarè rotation number theory, and the other of topological nature. |
| title | A new proof of Milnor-Wood inequality |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2412.14553 |