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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2601.11871 |
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| _version_ | 1866909993259761664 |
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| author | Park, Harahm |
| author_facet | Park, Harahm |
| contents | In this paper, we study contact structures supported by open book decompositions whose pages are four-punctured spheres. The paper is split into two parts. In the first part, we find infinitely many overtwisted, right-veering monodromies on the four-punctured sphere. This is done using the techniques developed by Ito-Kawamuro in the papers arXiv:1112.5874, arXiv:1310.6404. Although most of the monodromies that we show are overtwisted are pseudo-Anosov, we are also able to classify precisely which reducible monodromies on the four-punctured sphere are tight. In the second part of the paper, we reprove part of a result of Lekili arXiv:1008.3529 by classifying which reducible mondromies have non-zero Heegaard Floer invariant. This is done by using the bordered contact invariants of Min-Varvarezos arXiv:2410.05511. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11871 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Open book decompositions with page a four-punctured sphere Park, Harahm Geometric Topology In this paper, we study contact structures supported by open book decompositions whose pages are four-punctured spheres. The paper is split into two parts. In the first part, we find infinitely many overtwisted, right-veering monodromies on the four-punctured sphere. This is done using the techniques developed by Ito-Kawamuro in the papers arXiv:1112.5874, arXiv:1310.6404. Although most of the monodromies that we show are overtwisted are pseudo-Anosov, we are also able to classify precisely which reducible monodromies on the four-punctured sphere are tight. In the second part of the paper, we reprove part of a result of Lekili arXiv:1008.3529 by classifying which reducible mondromies have non-zero Heegaard Floer invariant. This is done by using the bordered contact invariants of Min-Varvarezos arXiv:2410.05511. |
| title | Open book decompositions with page a four-punctured sphere |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2601.11871 |