A note on three-fold branched covers of $S^4$
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2019
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| _version_ | 1866910611312476160 |
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| author | Blair, Ryan Cahn, Patricia Kjuchukova, Alexandra Meier, Jeffrey |
| author_facet | Blair, Ryan Cahn, Patricia Kjuchukova, Alexandra Meier, Jeffrey |
| contents | We show that any 4-manifold admitting a $(g;k_1,k_2,0)$-trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in $S^4$, smoothly embedded except for one singular point which is the cone on a link. A 4-manifold admits such a trisection if and only if it has a handle decomposition with no 1-handles; it is conjectured that all simply-connected 4-manifolds have this property. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1909_11788 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A note on three-fold branched covers of $S^4$ Blair, Ryan Cahn, Patricia Kjuchukova, Alexandra Meier, Jeffrey Geometric Topology 57M12, 57M25 We show that any 4-manifold admitting a $(g;k_1,k_2,0)$-trisection is an irregular 3-fold cover of the 4-sphere whose branching set is a surface in $S^4$, smoothly embedded except for one singular point which is the cone on a link. A 4-manifold admits such a trisection if and only if it has a handle decomposition with no 1-handles; it is conjectured that all simply-connected 4-manifolds have this property. |
| title | A note on three-fold branched covers of $S^4$ |
| topic | Geometric Topology 57M12, 57M25 |
| url | https://arxiv.org/abs/1909.11788 |