Homotopy of Operads and Grothendieck-Teichmuller Groups

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

• Homotopy theory and its applications to operads. General methods of homotopy theory: Model categories and homotopy theoryMapping spaces and simplicial model categoriesSimplicial structures and mapping spaces in general model categoriesCofibrantly generated model categoriesModules, algebras, and the rational homotopy of spaces: Differential graded modules, simplicial modules, and cosimplicial modulesDifferential graded algebras, simplicial algebras, and cosimplicial algebrasModels for the rational homotopy of spacesThe (rational) homotopy of operads: The model category of operads in simplicial setsThe homotopy theory of (Hopf) cooperadsModels for the rational homotopy of (non-unitary) operadsThe homotopy theory of (Hopf) $\Lambda$-cooperadsModels for the rational homotopy of unitary operadsApplications of the rational homotopy to $E_n$-operads: Complete Lie algebras and rational models of classifying spacesFormality and rational models of $E_n$-operadsThe computation of homotopy automorphism spaces of operads: Introduction to the results of the computations for the $E_n$-operadsThe applications of homotopy spectral sequences: Homotopy spsectral sequences and mapping spaces of operadsApplications of the cotriple cohomology of operadsApplications of the Koszul duality of operadsThe case of $E_n$-operads: The applications of the Koszul duality for $E_n$-operadsThe interpretation of the result of the spectral sequence in the case of $E_2$-operadsConclusion: A survey of further research on operadic mapping spaces and their applications: Graph complexes and $E_n$-operadsFrom $E_n$-operads to embedding spacesAppendices: Cofree cooperads and the bar duality of operadsGlossary of notationBibliographyIndex