Surfaces and their Profile Curves
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912705101692928 |
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| author | Hass, Joel |
| author_facet | Hass, Joel |
| contents | This paper examines the relationship between the knotting of an embedded surface in $\R^3$ and the knotting of its fold curves, formed by the singular set of projection to a plane. The first result shows that every surface, no matter how knotted, can be isotoped so that its fold curves form an unlink. A second result defines a new invariant which gives a complete obstruction to turning a fixed curve on a surface into a fold curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_01737 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Surfaces and their Profile Curves Hass, Joel Geometric Topology 57K10, 65D17, 53C45 This paper examines the relationship between the knotting of an embedded surface in $\R^3$ and the knotting of its fold curves, formed by the singular set of projection to a plane. The first result shows that every surface, no matter how knotted, can be isotoped so that its fold curves form an unlink. A second result defines a new invariant which gives a complete obstruction to turning a fixed curve on a surface into a fold curve. |
| title | Surfaces and their Profile Curves |
| topic | Geometric Topology 57K10, 65D17, 53C45 |
| url | https://arxiv.org/abs/2205.01737 |