Homotopy of Operads and Grothendieck Teichmuller Groups is popular PDF and ePub book, written by Benoit Fresse in 2017-05-22, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Homotopy of Operads and Grothendieck Teichmuller Groups can be Read Online from any device for your convenience.
Homotopy of Operads and Grothendieck Teichmuller Groups Book PDF Summary
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.
Detail Book of Homotopy of Operads and Grothendieck Teichmuller Groups PDF
- Author : Benoit Fresse
- Release : 22 May 2017
- Publisher : American Mathematical Soc.
- ISBN : 9781470434823
- Genre : Mathematics
- Total Page : 743 pages
- Language : English
- PDF File Size : 13,8 Mb
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