Invitation to Alexandrov geometry: CAT[0] spaces

Published 12 Jan 2017 in math.DG, math.AT, and math.MG | (1701.03483v3)

Abstract: The idea is to demonstrate the beauty and power of Alexandrov geometry by reaching interesting applications with a minimum of preparation. The topics include 1. Estimates on the number of collisions in billiards. 2. Construction of exotic aspherical manifolds. 3. The geometry of two-convex sets in Euclidean space.

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