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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1912.05672 |
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| _version_ | 1866909805123207168 |
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| author | Elgindi, Ali M. |
| author_facet | Elgindi, Ali M. |
| contents | Expanding on my former work along with the more recent work of Kasuya and Takase, we demonstrate that for a given link $L \subset M$ which is null-homologous in $H_1(M)$ and for any smooth oriented 2-plane field $η$ over $L$ there exists a smooth embedding $F:M \hookrightarrow \mathbb{C}^3$ so that the set of complex tangents to the embedding is exactly $L$ and at each $x \in L$ the holomorphic tangent space is exactly $η_x$. Furthermore, we demonstrate how the "analyticity" of a complex tangent, as given by the Bishop invariant, may be determined exactly from the angle formed between the holomorphic complex line and the the curve of complex tangents. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_05672 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Explicit Holomorphic Structures for embeddings of closed 3-manifolds into $\mathbb{C}^3$ Elgindi, Ali M. Complex Variables Geometric Topology Expanding on my former work along with the more recent work of Kasuya and Takase, we demonstrate that for a given link $L \subset M$ which is null-homologous in $H_1(M)$ and for any smooth oriented 2-plane field $η$ over $L$ there exists a smooth embedding $F:M \hookrightarrow \mathbb{C}^3$ so that the set of complex tangents to the embedding is exactly $L$ and at each $x \in L$ the holomorphic tangent space is exactly $η_x$. Furthermore, we demonstrate how the "analyticity" of a complex tangent, as given by the Bishop invariant, may be determined exactly from the angle formed between the holomorphic complex line and the the curve of complex tangents. |
| title | Explicit Holomorphic Structures for embeddings of closed 3-manifolds into $\mathbb{C}^3$ |
| topic | Complex Variables Geometric Topology |
| url | https://arxiv.org/abs/1912.05672 |