Authors: Živaljević, Rade 
Title: Topological methods in discrete geometry
Journal: Handbook of Discrete and Computational Geometry, Third Edition
First page: 551
Last page: 580
Issue Date: 1-Jan-2017
Rank: M13
ISBN: 978-149871139-5
DOI: 10.1201/9781315119601
A problem is solved or some other goal achieved by “topological methods” if in our arguments we appeal to the “form,” the “shape,” the “global” rather than “local” structure of the object or configuration space associated with the phenomenon we are interested in. This configuration space is typically a manifold or a simplicial complex. The global properties of the configuration space are usually expressed in terms of its homology and homotopy groups, which capture the idea of the higher (dis)connectivity of a geometric object and to some extent provide “an analysis properly geometric or linear that expresses location directly as algebra expresses magnitude.” 1.
Publisher: Taylor & Francis

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