**Mathematical Surveys and Monographs**

Volume: 217;
2017;
532 pp;
Hardcover

MSC: Primary 55;
Secondary 18; 57; 20

Print ISBN: 978-1-4704-3481-6

Product Code: SURV/217.1

List Price: $135.00

Individual Member Price: $108.00

**Electronic ISBN: 978-1-4704-3755-8
Product Code: SURV/217.1.E**

List Price: $135.00

Individual Member Price: $108.00

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#### Supplemental Materials

# Homotopy of Operads and Grothendieck–Teichmüller Groups: Part 1: The Algebraic Theory and its Topological Background

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*Benoit Fresse*

The Grothendieck–Teichmüller 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–Teichmüller
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

# Table of Contents

## Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 1: The Algebraic Theory and its Topological Background

#### Readership

Graduate students and researchers interested in algebraic topology and algebraic geometry.