On sections of maps from 4-manifolds to the 2-sphere
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911018860412928 |
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| author | Gompf, Robert E. |
| author_facet | Gompf, Robert E. |
| contents | This note exhibits singular fibrations over the 2-sphere whose regular fibers are connected surfaces of arbitrarily high genus, but which admit no sections. These include achiral Lefschetz fibrations, as well as generic maps for which some disks cannot lift to sections -- in fact, neither hemisphere lifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On sections of maps from 4-manifolds to the 2-sphere Gompf, Robert E. Geometric Topology 57K40 This note exhibits singular fibrations over the 2-sphere whose regular fibers are connected surfaces of arbitrarily high genus, but which admit no sections. These include achiral Lefschetz fibrations, as well as generic maps for which some disks cannot lift to sections -- in fact, neither hemisphere lifts. |
| title | On sections of maps from 4-manifolds to the 2-sphere |
| topic | Geometric Topology 57K40 |
| url | https://arxiv.org/abs/2506.18066 |