Real algebraic overtwisted contact structures on 3-spheres
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866908428972064768 |
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| author | Karadereli, Şeyma Öztürk, Ferit |
| author_facet | Karadereli, Şeyma Öztürk, Ferit |
| contents | A real algebraic link in the 3-sphere is defined as the zero locus in the 3-sphere of a real algebraic function from $\mathbb{R}^4$ to $\mathbb{R}^2$. A real algebraic open book decomposition on the 3-sphere is by definition the Milnor fibration of such a real algebraic function, in case it exists. We prove that every overtwisted contact structure on the 3-sphere with positive three dimensonal invariant $d_3$ (apart from possibly 9 exceptions) are real algebraic. Our construction shows in particular that the pages of the associated open books are planar. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_13305 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Real algebraic overtwisted contact structures on 3-spheres Karadereli, Şeyma Öztürk, Ferit Geometric Topology 57K33, 32S55 (Primary) 32C05 (Secondary) A real algebraic link in the 3-sphere is defined as the zero locus in the 3-sphere of a real algebraic function from $\mathbb{R}^4$ to $\mathbb{R}^2$. A real algebraic open book decomposition on the 3-sphere is by definition the Milnor fibration of such a real algebraic function, in case it exists. We prove that every overtwisted contact structure on the 3-sphere with positive three dimensonal invariant $d_3$ (apart from possibly 9 exceptions) are real algebraic. Our construction shows in particular that the pages of the associated open books are planar. |
| title | Real algebraic overtwisted contact structures on 3-spheres |
| topic | Geometric Topology 57K33, 32S55 (Primary) 32C05 (Secondary) |
| url | https://arxiv.org/abs/2205.13305 |