Singular fibrations over surfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911850040393728 |
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| author | Funar, Louis |
| author_facet | Funar, Louis |
| contents | Singular fibrations generalize achiral Lefschetz fibrations of 4-manifolds over surfaces while sharing some of their properties. For instance, relatively minimal singular fibrations are determined by their monodromy. We explain how to construct examples of singular fibrations with a single singularity and Matsumoto's construction of singular fibrations of the sphere $S^4$. Previous results of Hirzebruch and Hopf on 2-plane fields with finitely many singularities are outlined in connection with the work of Neumann and Rudolph on the Hopf invariant. Eventually, we prove that closed orientable 4-manifolds with large first Betti number and vanishing second Betti number do not admit singular fibrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_07018 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Singular fibrations over surfaces Funar, Louis Geometric Topology 57 R 45, 57 R 70 Singular fibrations generalize achiral Lefschetz fibrations of 4-manifolds over surfaces while sharing some of their properties. For instance, relatively minimal singular fibrations are determined by their monodromy. We explain how to construct examples of singular fibrations with a single singularity and Matsumoto's construction of singular fibrations of the sphere $S^4$. Previous results of Hirzebruch and Hopf on 2-plane fields with finitely many singularities are outlined in connection with the work of Neumann and Rudolph on the Hopf invariant. Eventually, we prove that closed orientable 4-manifolds with large first Betti number and vanishing second Betti number do not admit singular fibrations. |
| title | Singular fibrations over surfaces |
| topic | Geometric Topology 57 R 45, 57 R 70 |
| url | https://arxiv.org/abs/2202.07018 |