Coloured Koszul duality and strongly homotopy operads

Abstract

This paper proves Koszul duality for coloured operads and uses it to introduce strongly homotopy operads as a suitable homotopy invariant version of operads. It shows that rational chains on configuration spaces of points in the plane form a strongly homotopy operad quasi isomorphic to the chains on the little disks operad.

17 pages, 4 figures. V2: minor corrections

References in corpus (4)

• Operads, homotopy algebra and iterated integrals for double loop spaces
• Homotopy Diagrams of Algebras
• Homotopy Algebras are Homotopy Algebras
• Homotopy Inner Products for Cyclic Operads

Cited by in corpus (14)

• Deformation theory of representations of prop(erad)s
• Algebra+Homotopy=Operad
• Symmetric homotopy theory for operads
• A graphical category for higher modular operads
• Homotopy algebra of open-closed strings
• (Non-)formality of the extended Swiss Cheese operads
• Homotopy Inner Products for Cyclic Operads
• The diagonal of the operahedra
• Moduli problems for operadic algebras
• Combinatorial homotopy theory for operads
• Coextension of scalars in operad theory
• Operads and Maurer-Cartan spaces
• Reconnectads
• Compactified configuration space of points on a line and homotopies of $A_{\infty }$ morphisms