Combinatorial and Toric Homotopy: Introductory Lectures

Ebook Details


Alastair Darby, Jelena Grbic, Zhi Lü

Year 2017
Pages 448
Publisher World Scientific Publishing Co Pte Ltd
Language en
ISBN 9789813226562
File Size 5.95 MB
File Format PDF
Download Counter 178
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Ebook Description

The book starts intertwining homotopy theoretical and combinatorial ideas within the remits of toric topology and illustrates an attempt to classify in a combinatorial way polytopes known as fullerenes, which are important objects in quantum physics, quantum chemistry and nanotechnology. Toric homotopy theory is then introduced as a further development of toric topology, which describes properties of Davis Januszkiewicz spaces, moment-angle complexes and their generalizations to polyhedral products. The book also displays the current research on configuration spaces, braids, the theory of limits over the category of presentations and the theory of fr-codes. As an application to robotics, the book surveys topological problems relevant to the motion planning problem of robotics and includes new results and constructions, which enrich the emerging area of topological robotics.