Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry

A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. They are scattered in research papers or outlined in surveys, and they often use topological notions not commonly known among combinatorialists or computer scientists.

This book is the first textbook treatment of a significant part of such results. It focuses on so-called...