Patterns and Tracks

Abstract

Patterns in triangulated $2$-spheres and $3$-spheres are investigated. A reworking of the proof of Abigail Thompson of the Recognition Algorithm for $S^3$ is presented together with an explanation of how it can be adapted to give a short, self-contained proof of the Poincaré Conjecture.

15 pages, 17 figures. Minor changes and an extra reference