We define a new E∞ operad StLGT ree based on surfaces with foliations which contains Ek sub–operads. We construct CW models for these operads and provide applications of these models by giving actions on Hochschild complexes –thus making contact with string topology–, by giving explicit cell representatives for the Dyer-LashofCohen operations for the 2-cubes and by constructing new Ω spectra. T...

We analyze a functor from cyclic operads to chain complexes first considered by Getzler and Kapranov and also by Markl. This functor is a generalization of the graph homology considered by Kontsevich, which was defined for the three operads Comm, Assoc, and Lie. More specifically we show that these chain complexes have a rich algebraic structure in the form of families of operations defined by ...

We define and study a lift of the Boardman-Vogt tensor product of operads to bimodules over operads. Introduction Let Op denote the category of symmetric operads in the monoidal category S of simplicial sets. The Boardman-Vogt tensor product [3] −⊗− : Op× Op→ Op, which endows the category Op with a symmetric monoidal structure, codifies interchanging algebraic structures. For all P,Q ∈ Op, a (P...

We extend a result of M. M. Kapranov and Y. Manin concerning the Morita theory for linear operads. We also give a cyclic operad version of their result.

Introduction The following text arose from the desire to establish a rm relationship between higher order categories and topological spaces. Our approach combines the algebraic features of Michael Batanin's !-operads 1] with the geometric features of Andr e Joyal's cellular sets 15] and tries to mimick as far as possible the classical construction of the simplicial nerve of a category. Higher o...