Appears in collection : School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects

This series of lectures will describe recent and not-so-recent works in computational topology of curves in the plane and on surfaces. Combinatorial and algorithmic aspects will be discussed.

Lecture 2. Homotopy testing - definitions - polygons with holes: crossing sequence reduction - combinatorial surfaces - tree-cotree decomposition - Euler and discrete Gauss-Bonnet - universal cover - Dehn’s algorithms (classical and modern) - passing mention of Gromov hyperbolicity, CAT(0) spaces