Empire Maps on Surfaces
Geometric Topology
2011-06-22 v1
Abstract
This report is an introduction to mathematical map colouring and the problems posed by Heawood in his paper of 1890. There will be a brief discussion of the Map Colour Theorem; then we will move towards investigating empire maps in the plane and the recent contributions by Wessel. Finally we will conclude with a discussion of all known results for empire maps on higher genus surfaces and prove Heawoods Empire Conjecture in a previously unknown case.
Cite
@article{arxiv.1106.4235,
title = {Empire Maps on Surfaces},
author = {Caspar de Haes},
journal= {arXiv preprint arXiv:1106.4235},
year = {2011}
}
Comments
66 pages, 41 figures