Adem-Cartan operads

In this paper, we introduce Adem-Cartan operads and prove that the cohomology of any algebra over such an operad is an unstable level algebra over the extended Steenrod algebra. Moreover we prove that this cohomology is endowed with secondary cohomological operations.Comment: 26 pages, LaTeX. Replacemnet of "operadic description of Steenrod operations". It is a new approach (more conceptual) of the results of the previous pape

String topology of classifying spaces

Let G be a finite group or a compact connected Lie group and let BG be its classifying space. Let ℒBG ≔ map(S1, BG) be the free loop space of BG, i.e. the space of continuous maps from the circle S1 to BG. The purpose of this paper is to study the singular homology H*(ℒBG) of this loop space. We prove that when taken with coefficients in a field the homology of ℒBG is a homological conformal field theory. As a byproduct of our Main Theorem, we get a Batalin–Vilkovisky algebra structure on the cohomology H*(ℒBG). We also prove an algebraic version of this result by showing that the Hochschild cohomology HH*(S*(G), S*(G)) of the singular chains of G is a Batalin–Vilkovisky algebra.Comments (0

An operadic model for a mapping space and its associated spectral sequence

ArticleJOURNAL OF PURE AND APPLIED ALGEBRA. 210(2): 321-342 (2007)journal articl

Un modèle algébrique de la suite spectrale de Leray

Thanks to the notion of differential forms over an operad, we build a spectral sequence of Leray type. An application of this spectral sequence is the determination of the model of the fiber of a simplicial map, in the framework of epsilon (infinity)-algebras. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS