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Inventiones mathematicae, ISSN 1432-1297, 2018, Volume 216, Issue 1, pp. 1 - 68
We prove the validity over $${\mathbb {R}}$$ R of a commutative differential graded algebra model of configuration spaces for simply connected closed smooth... 
55P62 | Mathematics, general | Mathematics | 18D50 | 55R80 | MATHEMATICS | Analysis | Algebra | Mathematics - Algebraic Topology | Algebraic Topology
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 10/2017, Volume 49, Issue 5, pp. 824 - 830
It is proved that a compact nilmanifold endowed with a Vaisman structure is the product of N with S1, where N is a nilmanifold quotient of the Heisenberg group. 
55P62 | 53D35 (primary) | 53C55 | KAHLER-MANIFOLDS | MATHEMATICS
Journal Article
Journal of Topology, ISSN 1753-8416, 09/2018, Volume 11, Issue 3, pp. 666 - 719
We provide a universal de Rham model for rational G‐equivariant cohomology theories for an arbitrary torus G. More precisely, we show that the representing... 
55P62 | 55N91 | 55P42 | 55P91 (primary) | ADJUNCTIONS | MATHEMATICS | COHOMOLOGY | MODULE SPECTRA | CATEGORIES | HOMOTOPY THEORY | Mathematics - Algebraic Topology
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 12/2018, Volume 25, Issue 4, pp. 493 - 512
In this paper, we set up a rational homotopy theory for operads in simplicial sets whose term of arity one is not necessarily reduced to an operadic unit,... 
55P62 | rational homotopy | 18D50 | Sullivan models | Operads | 18G55 | MATHEMATICS | Mathematics - Algebraic Topology
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2018, Volume 288, Issue 3, pp. 1081 - 1101
... in dimensions 8 and 9. Keywords Rationally elliptic spaces · Rationally elliptic manifolds · Minimal models · Cohomology ring Mathematics Subject Classification Primary... 
Cohomology ring | Minimal models | Rationally elliptic manifolds | Mathematics, general | Mathematics | Rationally elliptic spaces | Primary 55P62 | Secondary 57R19 | MATHEMATICS | CURVATURE
Journal Article
manuscripta mathematica, ISSN 0025-2611, 5/2019, Volume 159, Issue 1, pp. 161 - 170
Let (L, d) be a differential graded Lie algebra, where $$L={\mathbb {L}}(V)$$ L = L ( V ) is free as graded Lie algebra and $$V=V_{\ge 0}$$ V = V ≥ 0 is a... 
Geometry | 16W60 | Topological Groups, Lie Groups | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | Number Theory | Primary 55P62 | Secondary 55P60 | MATHEMATICS | Analysis | Algebra | Mathematics - Algebraic Topology
Journal Article
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, ISSN 0025-5645, 10/2019, Volume 71, Issue 4, pp. 1153 - 1171
Kobayashi conjectured in the 36th Geometry Symposium in Japan (1989) that a homogeneous space G/H of reductive type does not admit a compact Clifford-Klein... 
EXISTENCE | MATHEMATICS | Clifford-Klein form | transgression | PROPER ACTIONS | HOMOGENEOUS SPACES | pure Sullivan algebra | relative Lie algebra cohomology
Journal Article
Journal of Homotopy and Related Structures, ISSN 2193-8407, 6/2016, Volume 11, Issue 2, pp. 309 - 332
By using homotopy transfer techniques in the context of rational homotopy theory, we show that if $$C$$ C is a coalgebra model of a space $$X$$ X , then the... 
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 | Mathematics - Algebraic Topology
Journal Article
Annali di Matematica Pura ed Applicata (1923 -), ISSN 0373-3114, 2/2019, Volume 198, Issue 1, pp. 61 - 81
For a compact complex manifold, we introduce holomorphic foliations associated with certain abelian subgroups of the automorphism group. If there exists a... 
Secondary 37F75 | Basic Dolbeault cohomology | Transverse Kähler structure | Primary 32Q55 | 58A14 | Central foliation | 55P62 | Mathematics, general | Mathematics | Basic cohomology | Mixed Hodge structure | 57N65 | MATHEMATICS | Transverse Kahler structure | MATHEMATICS, APPLIED | Computer science | Algebra | Scientists
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2017, Volume 286, Issue 3, pp. 1495 - 1524
We investigate the resonance varieties, lower central series ranks, and Chen ranks of the pure virtual braid groups and their upper-triangular subgroups. As an... 
Holonomy Lie algebra | Filtered-formality | 20J05 | 55P62 | Mathematics | Resonance varieties | Alexander invariants | Chen ranks | Pure virtual braid groups | Graded-formality | 20F40 | Primary 20F36 | 57M07 | Mathematics, general | Lower central series | 1-Formality | 20F14 | Secondary 16S37 | FINITE-TYPE INVARIANTS | LIE-ALGEBRA | VARIETIES | KNOTS | MATHEMATICS | COMPLETION | Algebra
Journal Article
Mathematische annalen, ISSN 1432-1807, 2005, Volume 334, Issue 3, pp. 533 - 555
... . Mathematics Subject Classification (2000): Primary: 20F36, 13F55, 20F14, 55P62, 57M07 1. Introduction 1.1. Right-angled Artin groups Let null = (V, E) be a nite simplicial... 
57M07 | 55P62 | Mathematics, general | Mathematics | 20F14 | 13F55 | Primary: 20F36 | MATHEMATICS | LOWER CENTRAL SERIES
Journal Article
Forum of mathematics. Sigma, ISSN 2050-5094, 2018, Volume 6
We consider smooth, complex quasiprojective varieties $U$ that admit a compactification with a boundary, which is an arrangement of smooth algebraic... 
Algebraic and Complex Geometry | MATHEMATICS | VARIETIES | CONFIGURATION-SPACES | MATHEMATICS, APPLIED | DUALITY | COHOMOLOGY | Homology | Hyperspaces | Algebra | Hyperplanes
Journal Article
Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 4/2017, Volume 23, Issue 1, pp. 257 - 265
In this note, it is shown that the Hilbert–Poincaré series for the rational homology of the free loop space on a moment-angle complex is a rational function if... 
55U10 | 55P35 | Rational homotopy | Free loop space | Secondary 52B11 | Rationally elliptic and hyperbolic | Davis–Januszkiewicz space | Mathematics, general | Mathematics | Moment-angle complex | Primary 55P62
Journal Article
Journal of Homotopy and Related Structures, ISSN 2193-8407, 9/2016, Volume 11, Issue 3, pp. 493 - 501
In this paper, we focus on Hilali’s conjecture that, for any simply-connected elliptic CW-complex X, the total sum of the rational Betti numbers is at least as... 
Rational homotopy theory | Algebra | Minimal models | Functional Analysis | Toral rank conjecture | Algebraic Topology | Mathematics | Coformal spaces | Number Theory | Primary 55P62 | Secondary 55T05 | MATHEMATICS
Journal Article
Journal of Pure and Applied Algebra, ISSN 0022-4049, 2010, Volume 214, Issue 10, pp. 1818 - 1826
We analyze k -stage formality and relate resonance with this type of formality properties. For instance, we show that, for a finitely generated nilpotent group... 
MATHEMATICS | MATHEMATICS, APPLIED | COMPLEMENT
Journal Article
Journal of topology, ISSN 1753-8416, 06/2020, Volume 13, Issue 2, pp. 539 - 575
We define the Bianchi–Massey tensor of a topological space X to be a linear map B→H∗(X), where B is a subquotient of H∗(X)⊗4 determined by the algebra H∗(X).... 
55P62 | 57R19 (primary) | MATHEMATICS | FORMALITY | CLASSIFICATION
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2013, Volume 273, Issue 3, pp. 981 - 997
We describe the rational homotopy type of any component of the based mapping space map*(X,Y) as an explicit L ∞ algebra defined on the (desuspended and... 
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
Geometriae Dedicata, ISSN 0046-5755, 8/2013, Volume 165, Issue 1, pp. 111 - 133
... Subject Classification Primary: 55P62 · 17B30 · Secondary: 22E25 · 11E04 1 Introduction and main theorem In this paper we classify some minimal algebras of dimension 7... 
Geometry | 11E04 | Minimal model | 17B30 | Rational homotopy | Nilmanifolds | Mathematics | Nilpotent Lie algebras | Primary: 55P62 | Secondary: 22E25 | MATHEMATICS | CLASSIFICATION | Analysis | Algebra
Journal Article
Afrika Matematika, ISSN 1012-9405, 9/2016, Volume 27, Issue 5, pp. 851 - 864
... type Mathematics Subject Classification Primary 55P62 · 55P15; Secondary 55P10 · 55Q05 · 55Q52 1 Introduction Two continuous maps f , g : X −→ Y are called... 
Rational homotopy theory | Rational homotopy type | Mathematics | History of Mathematical Sciences | 55Q52 | Primary 55P62 | Sullivan models | 55P15 | 55Q05 | Secondary 55P10 | Mathematics, general | Mathematics Education | Applications of Mathematics | Elliptic spaces
Journal Article
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