Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 1: The Algebraic Theory and its Topological Background (Mathematical Surveys and Monographs) - Hardcover

Fresse, Benoit

Hardcover

ISBN 10: 1470434814 ISBN 13: 9781470434816

Publisher: American Mathematical Society, 2017

Synopsis

The Grothendieck-Teichmuller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck-Teichmuller group from the viewpoint of the theory of operads. In the course of this study, the relationship between the little discs operads and the definition of universal operations associated to braided monoidal category structures is explained. Also provided is a comprehensive and self-contained survey of the applications of Hopf algebras to the definition of a rationalization process, the Malcev completion, for groups and groupoids. Most definitions are carefully reviewed in the book; it requires minimal prerequisites to be accessible to a broad readership of graduate students and researchers interested in the applications of operads.

About this title

About the Author

Benoit Fresse, Universite de Lille 1, Villeneuve d'Ascq, France.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2017
• Language: English
• ISBN 10: 1470434814
• ISBN 13: 9781470434816
• Binding: Hardcover
• Number of pages: 563