Homotopy of Operads and Grothendieck–Teichmüller Groups, Part 1: Part 1: The Algebraic Theory and its Topological Background
About this Title
Benoit Fresse, Université de Lille 1, Villeneuve d’Ascq, France
Publication: Mathematical Surveys and Monographs
Publication Year:
2017; Volume 217.1
ISBNs: 978-1-4704-3481-6 (print); 978-1-4704-3755-8 (online)
DOI: https://doi.org/10.1090/surv/217.1
MathSciNet review: MR3643404
MSC: Primary 55P48; Secondary 17B55, 18D50, 20F38, 20F40, 55P10, 55P62, 57T05
Table of Contents
Front/Back Matter
From operads to Grothendieck–Teichmüller groups
The general theory of operads
- The basic concepts of the theory of operads
- The definition of operadic composition structures revisited
- Symmetric monoidal categories and operads
Braids and $E_2$-operads
- The little discs model of $E_n$-operads
- Braids and the recognition of $E_2$-operads
- The magma and parenthesized braid operators
Hopf algebras and the Malcev completion
The operadic definition of the Grothendieck–Teichmüller group
- The Malcev completion of the braid operads and Drinfeld’s associators
- The Grothendieck–Teichmüller group
- A glimpse at the Grothendieck program
Appendices