Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 2: The Applications of (Rational) Homotopy Theory Methods (Mathematical Surveys and Monographs) - Hardcover

Fresse, Benoit

Hardcover

ISBN 10: 1470434822 ISBN 13: 9781470434823

Publisher: American Mathematical Society, 2017

Synopsis

The ultimate goal of this book is to explain that the Grothendieck-Teichmuller 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-Teichmuller 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.

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: 1470434822
• ISBN 13: 9781470434823
• Binding: Hardcover
• Number of pages: 715