Exotic elliptic surfaces without 1-handles
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915109491703808 |
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| author | Tange, Motoo |
| author_facet | Tange, Motoo |
| contents | In this article, we consider a sufficient condition that a knot-surgery or log-transformation of $E(n)$ admits a handle decomposition without 1-handles. We show that if $K$ is a knot that the bridge number is $b(K)\le 9n$, then the knot-surgery $E(n)_K$ of the elliptic surface $E(n)$ admits a handle decomposition without 1-handles. This means that if $\gcd(p,q)=1$, and $\min\{p,q\}\le 9$, then $E(1)_{p,q}$ admits a handle decomposition without 1-handles. We also show that if $\gcd (p,q)=1$, $\min\{p,q\}\le 4$, then the double log-transformation $E(n)_{p,q}$ admits a handle decomposition without 1-handles for any positive integer $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exotic elliptic surfaces without 1-handles Tange, Motoo Geometric Topology 57R65, 57R55 In this article, we consider a sufficient condition that a knot-surgery or log-transformation of $E(n)$ admits a handle decomposition without 1-handles. We show that if $K$ is a knot that the bridge number is $b(K)\le 9n$, then the knot-surgery $E(n)_K$ of the elliptic surface $E(n)$ admits a handle decomposition without 1-handles. This means that if $\gcd(p,q)=1$, and $\min\{p,q\}\le 9$, then $E(1)_{p,q}$ admits a handle decomposition without 1-handles. We also show that if $\gcd (p,q)=1$, $\min\{p,q\}\le 4$, then the double log-transformation $E(n)_{p,q}$ admits a handle decomposition without 1-handles for any positive integer $n$. |
| title | Exotic elliptic surfaces without 1-handles |
| topic | Geometric Topology 57R65, 57R55 |
| url | https://arxiv.org/abs/2501.03935 |