7 citations · 21 across the 13 of their papers we have counts for
15 papers
A Lie theoretic approach to the twisting procedure and Maurer-Cartan simplicial sets over arbitrary rings
Niek de Kleijn, Felix Wierstra
The Deligne-Getzler-Hinich---groupoid or Maurer-Cartan simplicial set of an -algebra plays an important role in deformation theory and many other areas of mathema…
Commutative homotopical algebra embeds into non-commutative homotopical algebra
Ricardo Campos, Dan Petersen, Daniel Robert-Nicoud +1
Over a field of characteristic zero, we show that the forgetful functor from the homotopy category of commutative dg algebras to the homotopy category of dg associative algebras is…
A recognition principle for iterated suspensions as coalgebras over the little cubes operad
Oisín Flynn-Connolly, José M. Moreno-Fernández, Felix Wierstra
Our main result is a recognition principle for iterated suspensions as coalgebras over the little disks operads. Given a topological operad, we construct a comonad in pointed topol…
On the homotopy fixed points of Maurer-Cartan spaces with finite group actions
José M. Moreno-Fernández, Felix Wierstra
We develop the basic theory of Maurer-Cartan simplicial sets associated to (shifted complete) algebras equipped with the action of a finite group. Our main result assert…
The simplicial coalgebra of chains determines homotopy types rationally and one prime at a time
Manuel Rivera, Felix Wierstra, Mahmoud Zeinalian
We prove that the simplicial cocommutative coalgebra of singular chains on a connected topological space determines the homotopy type rationally and one prime at a time, without im…
Iterated suspensions are coalgebras over the little disks operad
José M. Moreno-Fernández, Felix Wierstra
We study the Eckmann-Hilton dual of the little disks algebra structure on iterated loop spaces: With the right definitions, every -fold suspension is a coalgebra over the little…
Rational homotopy equivalences and singular chains
Manuel Rivera, Felix Wierstra, Mahmoud Zeinalian
Bousfield and Kan's -completion and fiberwise -completion of spaces lead to two different approaches to the rational homotopy theory of non-simply connected…
Lie, associative and commutative quasi-isomorphism
Ricardo Campos, Dan Petersen, Daniel Robert-Nicoud +1
Over a field of characteristic zero, we show that two commutative differential graded (dg) algebras are quasi-isomorphic if and only if they are quasi-isomorphic as associative dg…
-Hopf invariants
Felix Wierstra
The classical Hopf invariant is an invariant of homotopy classes of maps from to , and is an important invariant in homotopy theory. The goal of this paper is t…
Lie Theory for Complete Curved -algebras
Niek de Kleijn, Felix Wierstra
In this paper we develop the -analog of the Maurer-Cartan simplicial set associated to an -algebra and show how we can use this to study the deformation theory…
The functor of singular chains detects weak homotopy equivalences
Manuel Rivera, Felix Wierstra, Mahmoud Zeinalian
The normalized singular chains of a path connected pointed space may be considered as a connected -coalgebra with the property that the $0^{\text{…
Convolution algebras and the deformation theory of infinity-morphisms
Daniel Robert-Nicoud, Felix Wierstra
Given a coalgebra C over a cooperad, and an algebra A over an operad, it is often possible to define a natural homotopy Lie algebra structure on hom(C,A), the space of linear maps…
Homotopy morphisms between convolution homotopy Lie algebras
Daniel Robert-Nicoud, Felix Wierstra
In previous works by the authors, a bifunctor was associated to any operadic twisting morphism, taking a coalgebra over a cooperad and an algebra over an operad, and giving back th…
Hopf invariants and differential forms
Felix Wierstra
Let be two maps between simply-connected smooth manifolds and , such that is compact and is of finite -type. The goal of this paper…
Algebraic Hopf invariants and rational models for mapping spaces
Felix Wierstra
In this paper we will define an invariant of maps between a finite CW-complex and a rational space . We prove that…