**Mathematical Surveys and Monographs**

Volume: 217;
2017;
Hardcover

MSC: Primary 55;
Secondary 18; 57; 20

Print ISBN: 978-1-4704-3482-3

Product Code: SURV/217.2

List Price: $135.00

Individual Member Price: $108.00

**Electronic ISBN: 978-1-4704-3757-2
Product Code: SURV/217.2.E**

List Price: $135.00

Individual Member Price: $108.00

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# Homotopy of Operads and Grothendieck–Teichmüller Groups: Part 2: The Applications of (Rational) Homotopy Theory Methods

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*Benoit Fresse*

The ultimate goal of this book is to explain
that the Grothendieck–Teichmüller group, as defined by Drinfeld in
quantum group theory, has a topological interpretation as a group of
homotopy automorphisms associated to the little 2-disc operad. To
establish this result, the applications of methods of algebraic
topology to operads must be developed. This volume is devoted
primarily to this subject, with the main objective of developing a
rational homotopy theory for operads.

The book starts with a comprehensive review of the general theory
of model categories and of general methods of homotopy theory. The
definition of the Sullivan model for the rational homotopy of spaces
is revisited, and the definition of models for the rational homotopy
of operads is then explained. The applications of spectral sequence
methods to compute homotopy automorphism spaces associated to operads
are also explained. This approach is used to get a topological
interpretation of the Grothendieck–Teichmüller group in the
case of the little 2-disc operad.

This volume is intended for graduate students and researchers
interested in the applications of homotopy theory methods in operad
theory. It is accessible to readers with a minimal background in
classical algebraic topology and operad theory.

#### Table of Contents

# Table of Contents

## Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 2: The Applications of (Rational) Homotopy Theory Methods

#### Readership

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