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OverviewThe 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. Full Product DetailsAuthor: Benoit FressePublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 1.180kg ISBN: 9781470434816ISBN 10: 1470434814 Pages: 563 Publication Date: 30 May 2017 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsFrom operads to Grothendieck-Teichmuller groups. The general theory of operads: The basic concepts of the theory of operads The definition of operadic composition structures revisited Symmetric monoidal categories and operads Braids and $E_n$-operads: The little discs model of $E_n$-operads Braids and the recognition of $E_2$-operads The magma and parenthesized braid operators Hopf algebras and the Malcev completion: Hopf algebras The Malcev completion for groups The Malcev completion for groupoids and operads The operadic definition of the Grothendieck-Teichmuller group: The Malcev completion of the braid operads and Drinfeld's associators The Grothendieck-Teichmuller group A glimpse at the Grothendieck program Appendices: Trees and the construction of free operads The cotriple resolution of operads Glossary of notation Bibliography IndexReviewsAuthor InformationBenoit Fresse, Universite de Lille 1, Villeneuve d'Ascq, France. Tab Content 6Author Website:Countries AvailableAll regions |
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