Surfaces and their Profile Curves
Geometric Topology
2025-11-14 v2
Abstract
This paper examines the relationship between the knotting of an embedded surface in 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.
Cite
@article{arxiv.2205.01737,
title = {Surfaces and their Profile Curves},
author = {Joel Hass},
journal= {arXiv preprint arXiv:2205.01737},
year = {2025}
}
Comments
12 pages, 11 figures