Interlacement of double curves of immersed spheres
Geometric Topology
2017-04-20 v1 Combinatorics
Abstract
We characterize those unions of embedded disjoint circles in the 2-sphere which can be the multiple point set of a generic immersion of the 2-sphere into 3-dimensional space in terms of the interlacement of the given circles. Our result is the one higher dimensional analogue of Rosenstiehl's characterization of words being Gauss codes of self-crossing plane curves. Our proof uses a result of Lippner and we further generalize the ideas of Fraysseix and Ossona de Mendez, which leads us to directed interlacement graphs of paired trees and their local complementation.
Keywords
Cite
@article{arxiv.1704.05823,
title = {Interlacement of double curves of immersed spheres},
author = {Boldizsar Kalmar},
journal= {arXiv preprint arXiv:1704.05823},
year = {2017}
}
Comments
10 figures