Closures of T-homogeneous braids are real algebraic
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910955913347072 |
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| author | Bode, Benjamin |
| author_facet | Bode, Benjamin |
| contents | A link in $S^3$ is called real algebraic if it is the link of an isolated singularity of a polynomial map from $\mathbb{R}^4$ to $\mathbb{R}^2$. It is known that every real algebraic link is fibered and it is conjectured that the converse is also true. We prove this conjecture for a large family of fibered links, which includes closures of T-homogeneous (and therefore also homogeneous) braids and braids that can be written as a product of the dual Garside element and a positive word in the Birman-Ko-Lee presentation. The proof offers a construction of the corresponding real polynomial maps, which can be written as semiholomorphic functions. We obtain information about their polynomial degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_15394 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Closures of T-homogeneous braids are real algebraic Bode, Benjamin Geometric Topology Algebraic Geometry 57K10, 57R45, 32S55 A link in $S^3$ is called real algebraic if it is the link of an isolated singularity of a polynomial map from $\mathbb{R}^4$ to $\mathbb{R}^2$. It is known that every real algebraic link is fibered and it is conjectured that the converse is also true. We prove this conjecture for a large family of fibered links, which includes closures of T-homogeneous (and therefore also homogeneous) braids and braids that can be written as a product of the dual Garside element and a positive word in the Birman-Ko-Lee presentation. The proof offers a construction of the corresponding real polynomial maps, which can be written as semiholomorphic functions. We obtain information about their polynomial degrees. |
| title | Closures of T-homogeneous braids are real algebraic |
| topic | Geometric Topology Algebraic Geometry 57K10, 57R45, 32S55 |
| url | https://arxiv.org/abs/2211.15394 |