Empire Maps on Surfaces

Details Empire Maps on Surfaces Empire Maps on Surfaces

2011-06-21

arxiv.org/abs/1106.4235v1

Mathematics

Geometric Topology

66 pages, 41 figures

Scientific paper

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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