23 citations · 127 across the 26 of their papers we have counts for
30 papers
On the l-adic homotopy type of configuration spaces
Joana Cirici, Geoffroy Horel
We give algebraic models for the tame homotopy type of the configuration spaces of certain algebraic varieties of Tate type. Such tame models carry information on the l-adic homoto…
Equivariant formality of the little disks operad
Pedro Boavida de Brito, Joana Cirici, Geoffroy Horel
The little -disks operad is and -equivariantly formal over the rationals. Equivalently, the oriented and unoriented framed little disks operads are rationally form…
An algebro-geometric model for the configuration category
Pedro Boavida de Brito, Geoffroy Horel, Danica Kosanović
Using log-geometry, we construct a model for the configuration category of a smooth algebraic variety. As an application, we prove the formality of certain configuration spaces.
An operadic proof of the BTT Theorem
Joana Cirici, Geoffroy Horel
In this note, we explain an operadic proof of the BTT Theorem stating that the deformation theory of Calabi-Yau varieties is unobstructed. We also provide a short new proof of the…
E2 formality via obstruction theory
Geoffroy Horel
We attack the question of E_2-formality of differential graded algebras over prime fields via obstruction theory. We are able to prove that E_2-algebras whose cohomology ring is a…
Weight structures and formality
Coline Emprin, Geoffroy Horel
This is a survey on formality results relying on weight structures. A weight structure is a naturally occurring grading on certain differential graded algebras. If this weight sati…
Automorphisms of framed operads
Geoffroy Horel, Thomas Willwacher
Let be an operad acted upon by a group , and let be the corresponding framed operad. We relate the homotopy automorphism groups of $\m…
Formality of hypercommutative algebras of Kähler and Calabi-Yau manifolds
Joana Cirici, Geoffroy Horel
Any Batalin-Vilkovisky algebra with a homotopy trivialization of the BV-operator gives rise to a hypercommutative algebra structure at the cochain level which, in general, contains…
Binomial rings and homotopy theory
Geoffroy Horel
We produce a fully faithful functor from finite type nilpotent spaces to cosimplicial binomial rings, thus giving an algebraic model of integral homotopy types. As an application,…
Two remarks on spaces of maps between operads of little cubes
Geoffroy Horel, Manuel Krannich, Alexander Kupers
We record two facts on spaces of derived maps between the operads of little -cubes. Firstly, these mapping spaces are equivalent to the mapping spaces between the non-unit…
A multiplicative comparison of MacLane homology and topological Hochschild homology
Geoffroy Horel, Maxime Ramzi
Let denote MacLane's -construction, and denote the smash product of spectra. In this paper we construct an equivalence in the categ…
Motivic homological stability of configuration spaces
Geoffroy Horel, Martin Palmer
We prove that some of the classical homological stability results for configuration spaces of points in manifolds can be lifted to motivic cohomology.
Galois symmetries of knot spaces
Pedro Boavida de Brito, Geoffroy Horel
We exploit the Galois symmetries of the little disks operads to show that many differentials in the Goodwillie-Weiss spectral sequences approximating the homology and homotopy of k…
Homotopy transfer and formality
Gabriel C. Drummond-Cole, Geoffroy Horel
In a recent paper, the second author and Joana Cirici proved a theorem that says that given appropriate hypotheses, -formality of a differential graded algebraic structure is eq…
On the formality of the little disks operad in positive characteristic
Pedro Boavida de Brito, Geoffroy Horel
Using a variant of the Boardman-Vogt tensor product, we construct an action of the Grothendieck-Teichmüller group on the completion of the little n-disks operad . This action…
Etale cohomology, purity and formality with torsion coefficients
Joana Cirici, Geoffroy Horel
We use Galois group actions on étale cohomology to prove results of formality for dg-operads and dg-algebras with torsion coefficients. Our theory applies, among other related cons…
Operads of genus zero curves and the Grothendieck-Teichmüller group
Pedro Boavida de Brito, Geoffroy Horel, Marcy Robertson
We show that the group of homotopy automorphisms of the profinite completion of the genus zero surface operad is isomorphic to the (profinite) Grothendieck-Teichmüller group. Using…
Mixed Hodge structures and formality of symmetric monoidal functors
Joana Cirici, Geoffroy Horel
We use mixed Hodge theory to show that the functor of singular chains with rational coefficients is formal as a lax symmetric monoidal functor, when restricted to complex schemes w…
On two chain models for the gravity operad
Clément Dupont, Geoffroy Horel
In this note we recall the construction of two chain level lifts of the gravity operad, one due to Getzler-Kapranov and one due to Westerland. We prove that these two operads are f…
Automorphisms of the little disks operad with torsion coefficients
Geoffroy Horel
We compute the automorphisms of the Bousfield-Kan completion at a prime p of the little two-disks operads and show that they are given by the pro-p Grothendieck-Teichmüller group.…
Mixed Hodge structures and formality
Geoffroy Horel
We prove a formality theorem for algebraic objects internal to smooth complex varieties that are not compact but whose mixed Hodge structure has a certain purity property.
Motivic homological stability for configurations spaces of the line
Geoffroy Horel
We lift the classical theorem of Arnol'd on homological stability for configurations spaces of the plane to the motivic world. More precisely, we prove that the schemes of unordere…
Rigidification of higher categorical structures
Giovanni Caviglia, Geoffroy Horel
Given a limit sketch in which the cones have a finite connected base, we show that a model structure of "up to homotopy" models for this limit sketch in a suitable model category c…
Pro-categories in homotopy theory
Ilan Barnea, Yonatan Harpaz, Geoffroy Horel
The goal of this paper is to prove an equivalence between the model categorical approach to pro-categories, as studied by Isaksen, Schlank and the first author, and the -ca…