Empire Maps on Surfaces

Caspar de Haes

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arXiv · 1106.4235

Empire Maps on Surfaces

Caspar de Haes

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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.

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Caspar de Haes. 2011-06-21. Empire Maps on Surfaces. https://arxiv.org/abs/1106.4235

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