Urtzi Buijs

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20112024

most citedHomotopy theory of complete Lie algebras and Lie models of simplicial sets

17 citations · 60 across the 15 of their papers we have counts for

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20 papers · 1 filter

math.AT2024

Explicit Quillen models for Cartesian products of $2$ -cones

Urtzi Buijs, José Carrasquel, Lucile Vandembroucq

We give an explicit minimal Quillen model for the Cartesian product $X \times Y$ of rational $2$ -cones in terms of derivations and a binary operation $\star \colon \mathbb{M}(V)\oti…

math.AT2024

Sectional category à la Quillen

Urtzi Buijs, José Carrasquel

In this note we give a characterization of the sectional category of a map between rational spaces in terms of its Koszul-Quillen model.

math.AT2019

Formality criteria in terms of higher Whitehead brackets

Urtzi Buijs, José M. Moreno-Fernández

We provide two criteria for discarding the formality of a differential graded Lie algebra in terms of higher Whitehead brackets, which are the Lie analogue of the Massey products o…

math.AT2018

Rational maps from Euclidean Configuration Spaces to Spheres

Urtzi Buijs, Antonio Garvin, Aniceto Murillo

In this note we give an algorithm to determine the rational homotopy type of the free and pointed mapping spaces $ma p (F (R^{m}, k), S^{n})$ and $ma p^{*} (F (R^{m}, k), S^{n})$ .…

math.AT2018

Symmetric Lie models of a triangle

Urtzi Buijs, Yves Félix, Aniceto Murillo +1

R. Lawrence and D. Sullivan have constructed a Lie model for an interval from the geometrical idea of flat connections and flows of gauge transformations. Their model supports an a…

math.AT2018★ 5 cited

A-infinity structures and Massey products

Urtzi Buijs, José Manuel Moreno-Fernández, Aniceto Murillo

We show how and when it is possible to detect and recover higher Massey products on the cohomology $H$ of a differential graded algebra $A$ with higher multiplications on quasi-iso…

math.AT2017

$A_{\infty}$ structures and Massey products

José M. Moreno-Fernández

We study the relationship between the higher Massey products on the cohomology $H$ of a differential graded algebra, and the $A_{\infty}$ structures induced on $H$ via homotopy trans…

math.AT2017★ 6 cited

The infinity Quillen functor, Maurer-Cartan elements and DGL realizations

Urtzi Buijs, Yves Félix, Aniceto Murillo +1

We show an alternative construction of the cosimplicial free complete diferential graded Lie algebra $L_{∙} = L (s^{- 1} Δ^{∙})$ based on a new Lie…

math.AT2016

Weight decompositions of Thom spaces of vector bundles in rational homotopy theory

Urtzi Buijs, Federico Cantero Morán, Joana Cirici

Motivated by the theory of representability classes by submanifolds, we study the rational homotopy theory of Thom spaces of vector bundles. We first give a Thom isomorphism at the…

math.AT2016

Maurer-Cartan elements in the Lie models of finite simplicial complexes

Urtzi Buijs, Yves Félix, Aniceto Murillo +1

In a previous work, we have associated a complete differential graded Lie algebra to any finite simplicial complex in a functorial way. Similarly, we have also a realization functo…

math.AT2016★ 11 cited

Higher order Whitehead products and $L_{\infty}$ structures on the homology of a DGL

Francisco Belchí, Urtzi Buijs, José M. Moreno-Fernández +1

We detect higher order Whitehead products on the homology $H$ of a differential graded Lie algebra $L$ in terms of higher brackets in the transferred $L_{\infty}$ structure on $H$ vi…

math.AT2016★ 17 cited

Homotopy theory of complete Lie algebras and Lie models of simplicial sets

Urtzi Buijs, Yves Félix, Aniceto Murillo +1

In a previous work, by extending the classical Quillen construction to the non-simply connected case, we have built a pair of adjoint functors, 'model' and 'realization', between t…

math.AT2015

The Deligne groupoid of the Lawrence-Sullivan interval

Urtzi Buijs, Yves Félix, Aniceto Murillo +1

In this paper we completely describe the Deligne groupoid of the Lawrence-Sullivan interval as two parallel rational lines.

math.AT2015

Lie models of simplicial sets and representability of the Quillen functor

Urtzi Buijs, Yves Félix, Aniceto Murillo +1

Extending the model of the interval, we explicitly define for each $n \geq 0$ a free complete differential graded Lie algebra $L_{n}$ generated by the simplices of $Δ^{n}$ , wi…

math.AT2014★ 2 cited

The homotopy fixed point set of Lie group actions on elliptic spaces

Urtzi Buijs, Yves Félix, Sergio Huerta +1

Let $G$ be a compact connected Lie group, or more generally a path connected topological group of the homotopy type of a finite CW-complex, and let $X$ be a rational nilpotent $G$ -…

math.AT2012★ 4 cited

Homotopy transfer and rational models for mapping spaces

Urtzi Buijs, Javier J. Gutiérrez

By using homotopy transfer techniques in the context of rational homotopy theory, we show that if $C$ is a coalgebra model of a space $X$ , then the $A_{\infty}$ -coalgebra structure i…

math.AT2012★ 3 cited

$L_{i} n f t y$ rational homotopy of mapping spaces

Urtzi Buijs, Yves Félix, Aniceto Murillo

In this paper we describe explicit $L_{\infty}$ algebras modeling the rational homotopy type of any component of the spaces $\map(X,Y)$ and $\map^*(X,Y)$ of free and pointed maps bet…

math.AT2012★ 9 cited

The Lawrence-Sullivan construction is the right model of $I^{+}$

Urtzi Buijs, Aniceto Murillo

We prove that the universal enveloping algebra of the Lawrence-Sullivan construction is a particular perturbation of the complete Baues-Lemaire cylinder of $S^{0}$ . Together with oth…

math.AT2012★ 3 cited

Algebraic models of non-connected spaces and homotopy theory of $L_{\infty}$ algebras

Urtzi Buijs, Aniceto Murillo

We develop a homotopy theory of $L_{\infty}$ algebras based on the Lawrence-Sullivan construction, a complete differential graded Lie algebra which, as we show, satisfies the necessa…

math.AT2011

Rational Homotopy Type of the Classifying Space for Fibrewise Self-Equivalences

Urtzi Buijs, Samuel B. Smith

Let p be a fibration of simply connected CW complexes with finite base B and fibre F. Let aut_1(p) denote the identity component of the space of all fibre-homotopy self-equivalence…

Explicit Quillen models for Cartesian products of 2-cones

Sectional category à la Quillen

Formality criteria in terms of higher Whitehead brackets

Rational maps from Euclidean Configuration Spaces to Spheres

Symmetric Lie models of a triangle

A-infinity structures and Massey products

A∞​ structures and Massey products

The infinity Quillen functor, Maurer-Cartan elements and DGL realizations

Weight decompositions of Thom spaces of vector bundles in rational homotopy theory

Maurer-Cartan elements in the Lie models of finite simplicial complexes

Higher order Whitehead products and L∞​ structures on the homology of a DGL

Homotopy theory of complete Lie algebras and Lie models of simplicial sets

The Deligne groupoid of the Lawrence-Sullivan interval

Lie models of simplicial sets and representability of the Quillen functor

The homotopy fixed point set of Lie group actions on elliptic spaces

Homotopy transfer and rational models for mapping spaces

Li​nfty rational homotopy of mapping spaces

The Lawrence-Sullivan construction is the right model of I+

Algebraic models of non-connected spaces and homotopy theory of L∞​ algebras

Rational Homotopy Type of the Classifying Space for Fibrewise Self-Equivalences

Explicit Quillen models for Cartesian products of $2$ -cones

$A_{\infty}$ structures and Massey products

Higher order Whitehead products and $L_{\infty}$ structures on the homology of a DGL

$L_{i} n f t y$ rational homotopy of mapping spaces

The Lawrence-Sullivan construction is the right model of $I^{+}$

Algebraic models of non-connected spaces and homotopy theory of $L_{\infty}$ algebras