School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/)

Jeff Erickson (University of Illinois at Urbana-Champaign, USA)
Two-dimensional computational topology - Lecture 1

Abstract: 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.

1. Historical roots of computational topology
topological invariants, combinatorial encodings, and algorithms
angle sums, rotation numbers, regular homotopy
winding numbers, signed area, point-in-polygon
graphs and Euler tours
Gauss/Dowker code planarity

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