Title: Homotopy of Operads and Grothendieck Teichmuller Part 2: The Applications of (Rational) Homotopy Theory Methods
Publisher: Amer Mathematical Society
Publication Date: 2017
Language: English
ISBN 10: 1470434822
ISBN 13: 9781470434823
Binding: Hardcover
Condition: Brand New
Weight: 1.46 kilograms

About this title

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 the Author

Benoit Fresse, Universite de Lille 1, Villeneuve d'Ascq, France.

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