We study ordered configuration spaces of compact manifolds with boundary. We show that for a large class of such manifolds, the real homotopy type of the configuration spaces only depends on the real homotopy type of the pair consisting of the manifold and its
We develop a curved Koszul duality theory for algebras presented by quadratic-linear-constant relations over unital versions of binary quadratic operads. As an application, we study Poisson $n$-algebras given by polynomial functions on a standard shifted symplectic space. We compute explicit resolutions of these algebras
* Provides an in-depth discussion of the connection between operads and configuration spaces * Describes a unified and accessible approach to the use of graph complexes * Based on 4 lectures held in the framework of the Peccot Lecture and Prize by the Collège
In this paper we develop the combinatorics of leveled trees in order to construct explicit resolutions of (co)operads and (co)operadic (co)bimodules. We construct explicit cofibrant resolutions of operads and operadic bimodules in spectra analogous to the ordinary Boardman--Vogt resolutions and we express them as
We study bicolored configurations of points in the Euclidean $n$-space that are constrained to remain either inside or outside a fixed Euclidean $m$-subspace, with $n - m \ge 2$. We define a higher-codimensional variant of the Swiss-Cheese operad, called the complementarily constrained disks operad
We prove the validity over ℝ of a commutative differential graded algebra model of configuration spaces for simply connected closed smooth manifolds, answering a conjecture of Lambrechts--Stanley. We get as a result that the real homotopy type of such configuration spaces only depends on
We build a model in groupoids for the Swiss-Cheese operad, based on parenthesized permutations and braids, and we relate algebras over this model to the classical description of algebras over the homology of the Swiss-Cheese operad. We extend our model to a rational model
Nous donnons une introduction au domaine des opérades, des objets qui encodent les structures algébriques. Après les avoir définies, nous présentons plusieurs domaines d’application des opérades : espaces de lacets itérés, formalité, algèbres homotopiques, longs nœuds et groupe de Grothendieck--Teichmüller. --- Introductory work on
We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras on a fixed space $M$. This allows us to describe a notion of prefactorization algebra up to homotopy as well as morphisms
The Swiss-Cheese operads, which encode actions of algebras over the little $n$-cubes operad on algebras over the little $(n−1)$-cubes operad, comes in several variants. We prove that the variant in which open operations must have at least one open input is not formal in
We compute small rational models for configuration spaces of points on oriented surfaces, as right modules over the framed little disks operad. We do this by splitting these surfaces in unions of several handles. We first describe rational models for the configuration spaces of
We study configuration spaces of framed points on compact manifolds. Such configuration spaces admit natural actions of the framed little discs operads, that play an important role in the study of embedding spaces of manifolds and in factorization homology. We construct real combinatorial models
In a first part, we study Voronov's "Swiss-Cheese" operad $\mathsf{SC}_2$, which governs the action of a $\mathsf{D}_2$-algebra on a $\mathsf{D}_1$-algebra. We build a model in groupoids of this operad and we describe algebras over this model in a manner similar to the classical description
The main goal of this master's thesis is to define a complex computing the cohomology of Gerstenhaber algebras and associated deformation complexes using the iterated bar construction. Advisor: Benoit Fresse from Université de Lille.