Minimal genus trisection diagrams of the elliptic surfaces $E(n)$ via handle diagrams
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911741455106048 |
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| author | Isoshima, Tsukasa |
| author_facet | Isoshima, Tsukasa |
| contents | Lambert-Cole and Meier showed that the elliptic surface $E(n)$ admits a $(12n-2,0)$-trisection, considering the property that $E(n)$ is a certain double branched cover of $S^2 \times S^2$, which is a minimal genus trisection. In this paper, we clarify a way to construct an explicit $(12n-2,0)$-trisection diagram of $E(n)$ from its handle diagram arising from its Lefschetz fibration. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_02159 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimal genus trisection diagrams of the elliptic surfaces $E(n)$ via handle diagrams Isoshima, Tsukasa Geometric Topology Lambert-Cole and Meier showed that the elliptic surface $E(n)$ admits a $(12n-2,0)$-trisection, considering the property that $E(n)$ is a certain double branched cover of $S^2 \times S^2$, which is a minimal genus trisection. In this paper, we clarify a way to construct an explicit $(12n-2,0)$-trisection diagram of $E(n)$ from its handle diagram arising from its Lefschetz fibration. |
| title | Minimal genus trisection diagrams of the elliptic surfaces $E(n)$ via handle diagrams |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2606.02159 |