Advances in Mathematics, ISSN 0001-8708, 03/2013, Volume 236, pp. 60 - 91

We develop a homotopy theory of L∞ algebras based on the Lawrence–Sullivan construction, a complete differential graded Lie algebra which, as we show,...

Rational homotopy theory | [formula omitted]-algebras | Algebraic models of non-connected spaces | Maurer–Cartan set | algebras | Maurer-Cartan set | Analysis | Models | Algebra

Rational homotopy theory | [formula omitted]-algebras | Algebraic models of non-connected spaces | Maurer–Cartan set | algebras | Maurer-Cartan set | Analysis | Models | Algebra

Journal Article

Topology and its Applications, ISSN 0166-8641, 2012, Volume 159, Issue 3, pp. 721 - 732

In this paper, we describe an explicit L ∞ -algebra structure on the differential graded vector space of Lie γ-derivations between two differential graded Lie...

[formula omitted]-algebra | Rational homotopy theory | Mapping space | Sullivan model | Quillen model | Secondary | Primary | algebra

[formula omitted]-algebra | Rational homotopy theory | Mapping space | Sullivan model | Quillen model | Secondary | Primary | algebra

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 06/2013, Volume 141, Issue 6, pp. 2153 - 2167

is a double loop-space after rationalization.]]>

Lie derivation | Function space | Classifying space | Fibre-homotopy equivalences | Quillen model | MATHEMATICS | MATHEMATICS, APPLIED | classifying space | FIBRATIONS | MODELS | function space

Lie derivation | Function space | Classifying space | Fibre-homotopy equivalences | Quillen model | MATHEMATICS | MATHEMATICS, APPLIED | classifying space | FIBRATIONS | MODELS | function space

Journal Article

Topology and its Applications, ISSN 0166-8641, 11/2019, Volume 267, p. 106901

We provide two criteria for establishing the non-formality of a differential graded Lie algebra in terms of higher Whitehead brackets, which are the Lie...

Rational homotopy theory | [formula omitted]-algebra | Higher order Whitehead products | Coformality | Quillen spectral sequence | MATHEMATICS | MATHEMATICS, APPLIED | MODELS | PRODUCTS | SPACES | L-infinity-algebra | HOMOTOPY-THEORY

Rational homotopy theory | [formula omitted]-algebra | Higher order Whitehead products | Coformality | Quillen spectral sequence | MATHEMATICS | MATHEMATICS, APPLIED | MODELS | PRODUCTS | SPACES | L-infinity-algebra | HOMOTOPY-THEORY

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 05/2017, Volume 520, pp. 16 - 31

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∞ structure...

[formula omitted]-algebra | Rational homotopy theory | Higher Whitehead product | algebra

[formula omitted]-algebra | Rational homotopy theory | Higher Whitehead product | algebra

Journal Article

Journal of Homotopy and Related Structures, ISSN 2193-8407, 6/2016, Volume 11, Issue 2, pp. 309 - 332

...J. Homotopy Relat. Struct. (2016) 11:309–332 DOI 10.1007/s40062-015-0107-x Homotopy transfer and rational models for mapping spaces Urtzi Buijs 1 · Javier J...

Algebra | L_\infty $$ L ∞ -algebra | Functional Analysis | Mapping space | Secondary 54C35 | Algebraic Topology | Rational homotopy | Mathematics | Number Theory | Primary 55P62 | algebra | MATHEMATICS | L-infinity-algebra | LIE-ALGEBRA | HOMOLOGICAL ALGEBRA | WHITEHEAD PRODUCTS | CONE | L-INFINITY-ALGEBRAS | DEFORMATION-THEORY | Mathematics - Algebraic Topology

Algebra | L_\infty $$ L ∞ -algebra | Functional Analysis | Mapping space | Secondary 54C35 | Algebraic Topology | Rational homotopy | Mathematics | Number Theory | Primary 55P62 | algebra | MATHEMATICS | L-infinity-algebra | LIE-ALGEBRA | HOMOLOGICAL ALGEBRA | WHITEHEAD PRODUCTS | CONE | L-INFINITY-ALGEBRAS | DEFORMATION-THEORY | Mathematics - Algebraic Topology

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 10/2009, Volume 361, Issue 10, pp. 5601 - 5614

We give an explicit Lie model for any component of the space of free and pointed sections of a nilpotent fibration, and in particular, of the free and pointed...

Morphisms | Algebra | Mathematical theorems | Homotopy theory | Maps | Functors | Mathematical models | Vector space models | Vector spaces | Rational homotopy theory | Space of sections | Mapping space | Sullivan model | Quillen model | SPACE | MATHEMATICS | mapping space | RATIONAL HOMOTOPY-THEORY | rational homotopy theory

Morphisms | Algebra | Mathematical theorems | Homotopy theory | Maps | Functors | Mathematical models | Vector space models | Vector spaces | Rational homotopy theory | Space of sections | Mapping space | Sullivan model | Quillen model | SPACE | MATHEMATICS | mapping space | RATIONAL HOMOTOPY-THEORY | rational homotopy theory

Journal Article

Canadian mathematical bulletin, ISSN 0008-4395, 09/2017, Volume 60, Issue 3, pp. 470 - 477

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

Rational homotopy theory | Maurer-Cartan elements | Complete differential graded lie algebra | MATHEMATICS | complete differential graded Lie algebra | RATIONAL HOMOTOPY-THEORY | rational homotopy theory

Rational homotopy theory | Maurer-Cartan elements | Complete differential graded lie algebra | MATHEMATICS | complete differential graded Lie algebra | RATIONAL HOMOTOPY-THEORY | rational homotopy theory

Journal Article

Revista Matemática Complutense, ISSN 1139-1138, 7/2013, Volume 26, Issue 2, pp. 573 - 588

...Rev Mat Complut (2013) 26:573–588 DOI 10.1007/s13163-012-0105-z L ∞ rational homotopy of mapping spaces Urtzi Buijs · Yves Félix · Aniceto Murillo Received: 28...

Rational homotopy theory | 54C35 | 55P62 | Mathematics | Topology | L_\infty $$ algebra | Geometry | Algebra | Mapping space | Analysis | Mathematics, general | Applications of Mathematics | L_\infty $$ model of a space | L∞ algebra | L∞ model of a space

Rational homotopy theory | 54C35 | 55P62 | Mathematics | Topology | L_\infty $$ algebra | Geometry | Algebra | Mapping space | Analysis | Mathematics, general | Applications of Mathematics | L_\infty $$ model of a space | L∞ algebra | L∞ model of a space

Journal Article

Topology and its Applications, ISSN 0166-8641, 05/2016, Volume 204, pp. 1 - 7

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

Deligne groupoid | Lawrence–Sullivan inerval | Maurer–Cartan elements | Lawrence-Sullivan inerval | Maurer-Cartan elements

Deligne groupoid | Lawrence–Sullivan inerval | Maurer–Cartan elements | Lawrence-Sullivan inerval | Maurer-Cartan elements

Journal Article

Journal of Topology, ISSN 1753-8416, 09/2018, Volume 11, Issue 3, pp. 799 - 825

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...

17B55 | 55U10 (secondary) | 55P62 (primary) | MATHEMATICS | SPACES | Mathematics - Algebraic Topology

17B55 | 55U10 (secondary) | 55P62 (primary) | MATHEMATICS | SPACES | Mathematics - Algebraic Topology

Journal Article

Forum Mathematicum, ISSN 0933-7741, 03/2017, Volume 29, Issue 2, pp. 277 - 286

In this paper we prove a family of identities for Bernoulli numbers parameterized by triples of integers with , . These identities are deduced by translating...

17B01 | 55U35 | Bernoulli numbers | homotopy theory of Lie algebras | 11B68 | Gauge action | MATHEMATICS | MATHEMATICS, APPLIED | MODELS

17B01 | 55U35 | Bernoulli numbers | homotopy theory of Lie algebras | 11B68 | Gauge action | MATHEMATICS | MATHEMATICS, APPLIED | MODELS

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 05/2015, Volume 110, Issue 5, pp. 1135 - 1156

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...

MATHEMATICS | SECTIONS | MODELS | RATIONAL HOMOTOPY | Fixed points (mathematics) | Algebra | Equivalence | Mathematical analysis | Lie groups | Mathematical models | Topology | Inclusions | Formulas (mathematics) | Mathematics - Algebraic Topology

MATHEMATICS | SECTIONS | MODELS | RATIONAL HOMOTOPY | Fixed points (mathematics) | Algebra | Equivalence | Mathematical analysis | Lie groups | Mathematical models | Topology | Inclusions | Formulas (mathematics) | Mathematics - Algebraic Topology

Journal Article

Algebraic and Geometric Topology, ISSN 1472-2747, 03/2013, Volume 13, Issue 1, pp. 577 - 588

We prove that the universal enveloping algebra of the Lawrence-Sullivan construction is a particular perturbation of the complete Baues-Lemaire cylinder of...

MATHEMATICS | COMPONENTS

MATHEMATICS | COMPONENTS

Journal Article

Commentarii Mathematici Helvetici, ISSN 0010-2571, 2008, Volume 83, p. 723

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2011, Volume 63, Issue 2, pp. 503 - 524

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 4/2013, Volume 273, Issue 3, pp. 981 - 997

... mapping cone Urtzi Buijs · Javier J. Gutiérrez · Aniceto Murillo Dedicated to Yves Félix, on his 60th birthday Received: 29 November 2011 / Accepted: 3 April 2012...

Mapping space | Secondary 54C35 | Rational homotopy | Mathematics, general | Mathematics | Primary 55P62 | L ∞ -algebras | algebras | MATHEMATICS | LIE-ALGEBRA | MODELS | L infinity-algebras | Analysis | Algebra

Mapping space | Secondary 54C35 | Rational homotopy | Mathematics, general | Mathematics | Primary 55P62 | L ∞ -algebras | algebras | MATHEMATICS | LIE-ALGEBRA | MODELS | L infinity-algebras | Analysis | Algebra

Journal Article

Commentarii Mathematici Helvetici, ISSN 0010-2571, 2008, Volume 83, Issue 4, pp. 723 - 739

In this paper we fully describe the rational homotopy Lie algebra of any component of a given (free or pointed) function space. Also, we characterize higher...

General | Algebraic topology | General topology | Rational homotopy theory | Homotopy Lie algebra | Function space | Sullivan model | NILPOTENT BUNDLE | MATHEMATICS | MODELS | CATEGORY | SECTIONS | homotopy Lie algebra | rational homotopy theory

General | Algebraic topology | General topology | Rational homotopy theory | Homotopy Lie algebra | Function space | Sullivan model | NILPOTENT BUNDLE | MATHEMATICS | MODELS | CATEGORY | SECTIONS | homotopy Lie algebra | rational homotopy theory

Journal Article

Israel journal of mathematics, ISSN 0021-2172, 06/2020

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2009, Volume 222, Issue 1, pp. 151 - 171

In this paper, when G is the circle S 1 and M is a G-space, we study the rational homotopy type of the fixed point set M G , the homotopy fixed point set M h G...

Space of sections | Fixed point set | Homotopy fixed point set | Rational homotopy | BUNDLE | MATHEMATICS | FUNCTION-SPACES | MAPS

Space of sections | Fixed point set | Homotopy fixed point set | Rational homotopy | BUNDLE | MATHEMATICS | FUNCTION-SPACES | MAPS

Journal Article

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