172 citations · 376 across the 25 of their papers we have counts for
24 papers · 1 filter
On a notion of homotopy Segal -Hopf cooperad
Benoit Fresse, Lorenzo Guerra
We define a notion of homotopy Segal cooperad in the category of -algebras. This model of Segal cooperad that we define in the paper, which we call homotopy Segal $ E_\…
On the rational homotopy type of embedding spaces of manifolds in
Benoit Fresse, Victor Turchin, Thomas Willwacher
We study the spaces of embeddings of manifolds in a Euclidean space. More precisely we look at the homotopy fiber of the inclusion of these spaces to the spaces of immersions. As a…
Mapping Spaces for DG Hopf Cooperads and Homotopy Automorphisms of the Rationalization of -operads
Benoit Fresse, Thomas Willwacher
We define a simplicial enrichment on the category of differential graded Hopf cooperads (the category of dg Hopf cooperads for short). We prove that our simplicial enrichment satis…
Projective and Reedy model category structures for (infinitesimal) bimodules over an operad
Julien Ducoulombier, Benoit Fresse, Victor Turchin
We construct and study projective and Reedy model category structures for bimodules and infinitesimal bimodules over topological operads. Both model structures produce the same hom…
Little discs operads, graph complexes and Grothendieck--Teichmüller groups
Benoit Fresse
This paper is a survey on the homotopy theory of -operads written for the new handbook of homotopy theory.
The extended rational homotopy theory of operads
Benoit Fresse
In this paper, we set up a rational homotopy theory for operads in simplicial sets whose term of arity one is not necessarily reduced to an operadic unit, extending results obtaine…
The homotopy theory of operad subcategories
Benoit Fresse, Victor Turchin, Thomas Willwacher
We study the subcategory of topological operads such that (the category of unitary operads in our terminology). We use that this category inherits a model structure,…
The intrinsic formality of -operads
Benoit Fresse, Thomas Willwacher
We establish that -operads satisfy a rational intrinsic formality theorem for . We gain our results in the category of Hopf cooperads in cochain graded dg-modules whi…
The cotriple resolution of differential graded algebras
Benoit Fresse
We consider the cotriple resolution of algebras over operads in differential graded modules. We focus, to be more precise, on the example of algebras over the differential graded B…
Iterated bar complexes and E_n-homology with coefficients
Benoit Fresse, Stephanie Ziegenhagen
The first author proved in a previous paper that the n-fold bar construction for commutative algebras can be generalized to E_n-algebras, and that one can calculate E_n-homology wi…
Idempotents, Localizations and Picard groups of A(1)-modules
Robert R. Bruner
We analyze the stable isomorphism type of polynomial rings on degree 1 generators as modules over the sub-algebra A(1) = <Sq^1, Sq^2> of the mod 2 Steenrod algebra. Since their aug…
Koszul duality complexes for the cohomology of iterated loop spaces of spheres
Benoit Fresse
The goal of this article is to make explicit a structured complex whose homology computes the cohomology of the p-profinite completion of the n-fold loop space of a sphere of dimen…
On mapping spaces of differential graded operads with the commutative operad as target
Benoit Fresse
The category of differential graded operads is a cofibrantly generated model category and as such inherits simplicial mapping spaces. The vertices of an operad mapping space are ju…
Koszul duality of E_n-operads
Benoit Fresse
The goal of this paper is to prove a Koszul duality result for E_n-operads in differential graded modules over a ring. The case of an E_1-operad, which is equivalent to the associa…
Operadic bar constructions, cylinder objects, and homotopy morphisms of algebras over operads
Benoit Fresse
The purpose of this paper is twofold. First, we review applications of the bar duality of operads to the construction of explicit cofibrant replacements in categories of algebras o…
Props in model categories and homotopy invariance of structures
Benoit Fresse
We prove that any category of props in a symmetric monoidal model category inherits a model structure. We devote an appendix, about half the size of the paper, to the proof of the…
Modules over operads and functors
Benoit Fresse
In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically tha…
The universal Hopf operads of the bar construction
Benoit Fresse
The goal of this memoir is to prove that the bar complex B(A) of an E-infinity algebra A is equipped with the structure of a Hopf E-infinity algebra, functorially in A. We observe…
The bar complex of an E-infinity algebra
Benoit Fresse
The standard reduced bar complex B(A) of a differential graded algebra A inherits a natural commutative algebra structure if A is a commutative algebra. We address an extension of…
The bar construction of an algebra as an E-infinite Hopf algebra
Benoit Fresse
We prove that the bar construction of an algebra forms an algebra. To be more precise, we provide the bar construction of an algebra over the surjection opera…
Koszul duality of operads and homology of partition posets
Benoit Fresse
We consider partitions of a set with elements ordered by refinement. We consider the simplicial complex formed by chains of partitions which starts at the smallest…
Derived division functors and mapping spaces
Benoit Fresse
The normalized cochain complex of a simplicial set N^*(Y) is endowed with the structure of an E_{infinity} algebra. More specifically, we prove in a previous article that N^*(Y) is…
A prismatic decomposition of the Barratt-Eccles operad
Clemens Berger, Benoit Fresse
The Barratt-Eccles operad is a simplicial operad formed by the classical homogeneous bar construction of the symmetric groups. We prove that these simplicial sets decompose as unio…
Combinatorial operad actions on cochains
Clemens Berger, Benoit Fresse
A classical E-infinity operad is formed by the bar construction of the symmetric groups. Such an operad has been introduced by M. Barratt and P. Eccles in the context of simplicial…