Combinatorial and Toric Homotopy

Introductory Lectures

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book Combinatorial and Toric Homotopy by Alastair Darby, Jelena Grbić, Zhi Lü;Jie Wu, World Scientific Publishing Company
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Author: Alastair Darby, Jelena Grbić, Zhi Lü;Jie Wu ISBN: 9789813226586
Publisher: World Scientific Publishing Company Publication: October 20, 2017
Imprint: WSPC Language: English
Author: Alastair Darby, Jelena Grbić, Zhi Lü;Jie Wu
ISBN: 9789813226586
Publisher: World Scientific Publishing Company
Publication: October 20, 2017
Imprint: WSPC
Language: English

This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning.

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.

The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students.

Contents:

  • Toric Homotopy Theory (Stephen Theriault)
  • Fullerenes, Polytopes and Toric Topology (Victor M Buchstaber and Nikolay Yu Erokhovets)
  • Around Braids (Vladimir Vershinin)
  • Higher Limits, Homology Theories and fr-Codes (Sergei O Ivanov and Roman Mikhailov)
  • Configuration Spaces and Robot Motion Planning Algorithms (Michael Farber)
  • Cellular Stratified Spaces (Dai Tamaki)

Readership: Advanced undergraduate and graduate students as well as researchers interested in homotopy theory and its applications in the sciences.
Key Features:

  • The first book in the area of toric homotopy theory consisting of introductory lectures on the topics and their applications to fr-codes and robot motion planning
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This volume consists of introductory lectures on the topics in the new and rapidly developing area of toric homotopy theory, and its applications to the current research in configuration spaces and braids, as well as to more applicable mathematics such as fr-codes and robot motion planning.

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.

The book is at research entry level addressing the core components in homotopy theory and their important applications in the sciences and thus suitable for advanced undergraduate and graduate students.

Contents:

Readership: Advanced undergraduate and graduate students as well as researchers interested in homotopy theory and its applications in the sciences.
Key Features:

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