The algebraic theory and its topological background

Author(s)

• Fresse, Benoit

Bibliographic Information

The algebraic theory and its topological background

Benoit Fresse

（Mathematical surveys and monographs, v. 217 . Homotopy of operads and Grothendieck-Teichmüller groups ; pt. 1）

American Mathematical Society, c2017

Note

Includes bibliographical references (p. 511-520) and index

Description and Table of Contents

Description

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.

Table of Contents

From 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 Index

by "Nielsen BookData"

Details

• NCID: BB23720473
• ISBN:
  • 9781470434816
• LCCN: 2016032055
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: xlvi, 532 p.
• Size: 26 cm
• Classification:
  • LCC : QA612.7
  • DC23 : 514/.24
• Subject Headings:
  • LCSH : Homotopy theory
  • LCSH : Operads
  • LCSH : Grothendieck groups
  • LCSH : Teichmüller spaces
• Parent Bibliography ID:
  • BA00134419