We define a generalization of Massey products for algebras over Koszul operad in characteristic zero, extending Massey’s and Allday’s Retah’s the associative Lie cases, respectively. establish connections with minimal models Dimitrova’s universal operadic cohomology class. compute Gerstenhaber algebra example hypercommutative related to Chevalley–Eilenberg complex Heisenberg algebra.

Every homology or cohomology theory on a category ofE∞ ring spectra is Topological André–Quillen homology or cohomology with appropriate coefficients. Analogous results hold more generally for categories of algebras over operads. Mathematics Subject Classification (2000): 55P43, 55P48, 55U35

We define several differential graded operads, some of them being related to families of polytopes : simplices and permutohedra. We also obtain a presentation by generators and relations of the operad K on associahedra introduced in a previous article.

We define a plus-construction on connective augmented algebras over operads in symmetric spectra using Quillen homology. For associative and commutative algebras, we show that this plus-construction is related to both Bousfield localization and Carlsson’s derived completion.

We study a connection between mapping spaces of bimodules and infinitesimal over an operad. As main application motivation our work, we produce explicit delooping the manifold calculus tower associated to space smooth maps D m → n $D^m\rightarrow D^n$ discs, ⩾ $n\geqslant m$ , avoiding any given multisingularity coinciding with standard inclusion near boundary ∂ $\partial D^m$ . In particular, ...