On Negami's planar cover conjecture
Combinatorics
2007-05-23 v1 Geometric Topology
Abstract
Given a finite cover f:tilde{G} \to G and an embedding of tilde{G} in the plane, Negami conjectures that G embeds in P^2. Negami proved this conjecture for regular covers. In this paper we define two properties (Propserties V and E), depending on the cover tilde{G} and its embedding into S^2, and generalize Negami's result by showing: (1) If Properties V and E are fulfilled then G embeds in P^2. (2) Regular covers always fulfill Properties V and E. We give an example of an irregular cover fulfilling Properties V and E. Covers not fulfilling Properties V and E are discussed as well.
Cite
@article{arxiv.math/0612342,
title = {On Negami's planar cover conjecture},
author = {Yo'av Rieck and Yasushi Yamashita},
journal= {arXiv preprint arXiv:math/0612342},
year = {2007}
}
Comments
20 pages, 13 figures