Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.01737 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912705101692928 |
|---|---|
| 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 |