Algebraic Topology

A first course in Algebraic Topology, with emphasis on visualization, geometric intuition and simplified computations. Given by Assoc Prof N J Wildberger at UNSW. The really important aspect of a course in Algebraic Topology is that it introduces us to a wide range of novel objects: the sphere, torus, projective plane, knots, Klein bottle, the circle, polytopes, curves in a way that disregards many of the unessential features, and only retains the essence of the shapes of spaces. What does this exactly mean? That is a key question… The course has some novel features, including Conway’s ZIP proof of the classification of surfaces, a rational form of turn angles and curvature, an emphasis on the importance of the rational line as the model of the continuum, and a healthy desire to keep things simple and physical. We try to use pictures and models to guide our understanding.

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