On elliptic surfaces which have no 1-handles
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912081744232448 |
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| author | Kusuda, Daisuke |
| author_facet | Kusuda, Daisuke |
| contents | Gompf conjectured that the elliptic surface $E(n)_{p,q}$ has no handle decomposition without 1- and 3-handles. We prove that each of the elliptic surfaces $E(n)_{5,6}$, $E(n)_{6,7}$, $E(n)_{7,8}$ and $E(n)_{8,9}$ has a handle decomposition without 1-handles for $n\geq4$, $n\geq 5$, $n\geq 9$ and $n\geq 24$, respectively. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_16900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On elliptic surfaces which have no 1-handles Kusuda, Daisuke Geometric Topology 57R55, 57R19 Gompf conjectured that the elliptic surface $E(n)_{p,q}$ has no handle decomposition without 1- and 3-handles. We prove that each of the elliptic surfaces $E(n)_{5,6}$, $E(n)_{6,7}$, $E(n)_{7,8}$ and $E(n)_{8,9}$ has a handle decomposition without 1-handles for $n\geq4$, $n\geq 5$, $n\geq 9$ and $n\geq 24$, respectively. |
| title | On elliptic surfaces which have no 1-handles |
| topic | Geometric Topology 57R55, 57R19 |
| url | https://arxiv.org/abs/2410.16900 |