Manuscripta Mathematica, ISSN 0025-2611, 05/2017, Volume 153, Issue 1-2, pp. 231 - 262

Journal Article

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

55P62 | Mathematics, general | Mathematics | 18D50 | 55R80 | MATHEMATICS | Analysis | Algebra | Mathematics - Algebraic Topology | Algebraic Topology

Journal Article

Arabian Journal of Mathematics, ISSN 2193-5343, 12/2016, Volume 5, Issue 4, pp. 225 - 237

Let a simply-connected homogeneous space $${X}$$ X satisfy the condition of $${{\rm dim} \pi_{\rm even}(X)\otimes {\mathbb{Q}}=2}$$ dim π even ( X ) ⊗ Q = 2...

55P62 | Mathematics, general | 55R15 | Mathematics

55P62 | Mathematics, general | 55R15 | Mathematics

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

55P62 | rational homotopy | 18D50 | Sullivan models | Operads | 18G55 | MATHEMATICS | Mathematics - Algebraic Topology

Journal Article

Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 4/2017, Volume 23, Issue 1, pp. 267 - 288

Let X be a connected topological spaces with finite rational Betti numbers. We denote by G the radical of its fundamental group and by $$(\wedge V,d)$$ ( ∧ V ,...

55P62 | Mathematics, general | 55Q05 | Mathematics | 17B30

55P62 | Mathematics, general | 55Q05 | Mathematics | 17B30

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

55P62 | 53D35 (primary) | 53C55 | KAHLER-MANIFOLDS | MATHEMATICS

Journal Article

Journal of the London Mathematical Society, ISSN 0024-6107, 02/2019, Volume 99, Issue 1, pp. 173 - 193

Does a space enjoying good finiteness properties admit an algebraic model with commensurable finiteness properties? In this note, we provide a rational...

17B01 | 55P62 (primary) | 55N25 (secondary) | 20F14 | 20J05 | TOPOLOGY | MATHEMATICS | VARIETIES | JUMP LOCI | GEOMETRY

17B01 | 55P62 (primary) | 55N25 (secondary) | 20F14 | 20J05 | TOPOLOGY | MATHEMATICS | VARIETIES | JUMP LOCI | GEOMETRY

Journal Article

Georgian Mathematical Journal, ISSN 1072-947X, 06/2019, Volume 26, Issue 2, pp. 311 - 314

Here is a sketch of a few of the connections between Prof. Nodar Berikashvili and his school and higher homotopy structures.

55U99 | 81T13 | cohomological physics | 55R20 | Twisting cochains | higher homotopy structures | 55P62

55U99 | 81T13 | cohomological physics | 55R20 | Twisting cochains | higher homotopy structures | 55P62

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

55P62 | 55N91 | 55P42 | 55P91 (primary) | ADJUNCTIONS | MATHEMATICS | COHOMOLOGY | MODULE SPECTRA | CATEGORIES | HOMOTOPY THEORY | Mathematics - Algebraic Topology

Journal Article

Geometriae Dedicata, ISSN 0046-5755, 6/2016, Volume 182, Issue 1, pp. 215 - 232

The Hirzebruch signature formula provides an obstruction to the following realization question: given a rational Poincaré duality algebra $${\mathcal {A}}$$ A...

Geometry | Rational homotopy type | Manifold | Surgery | 55P62 | Mathematics | Characteristic classes and numbers | 57R65 | 57R20 | 57N65

Geometry | Rational homotopy type | Manifold | Surgery | 55P62 | Mathematics | Characteristic classes and numbers | 57R65 | 57R20 | 57N65

Journal Article

11.
Full Text
Classification and characterization of rationally elliptic manifolds in low dimensions

Mathematische Zeitschrift, ISSN 0025-5874, 4/2018, Volume 288, Issue 3, pp. 1081 - 1101

We give a characterization of closed, simply connected, rationally elliptic 6-manifolds in terms of their rational cohomology rings and a partial...

Cohomology ring | Minimal models | Rationally elliptic manifolds | Mathematics, general | Mathematics | Rationally elliptic spaces | Primary 55P62 | Secondary 57R19 | MATHEMATICS | CURVATURE

Cohomology ring | Minimal models | Rationally elliptic manifolds | Mathematics, general | Mathematics | Rationally elliptic spaces | Primary 55P62 | Secondary 57R19 | MATHEMATICS | CURVATURE

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

Georgian Mathematical Journal, ISSN 1072-947X, 12/2018, Volume 25, Issue 4, pp. 545 - 570

Kadeishvili proposes a minimal -algebra as a rational homotopy model of a space. We discuss a cyclic version of this Kadeishvili -model and apply it to...

Poincaré duality | 55U35 | 55S30 | Homotopy algebras | 55P62 | 18G55 | rational homotopy theory | MATHEMATICS | COHOMOLOGY | Poincare duality | POINCARE-DUALITY | A-INFINITY-ALGEBRAS

Poincaré duality | 55U35 | 55S30 | Homotopy algebras | 55P62 | 18G55 | rational homotopy theory | MATHEMATICS | COHOMOLOGY | Poincare duality | POINCARE-DUALITY | A-INFINITY-ALGEBRAS

Journal Article

Forum Mathematicum, ISSN 0933-7741, 03/2017, Volume 29, Issue 2, pp. 251 - 257

In this short note we observe that the Hilali conjecture holds for 2-stage spaces, i.e. we argue that the dimension of the rational cohomology is at least as...

55P62 | 55Q52 | rational cohomology groups | Hilali conjecture | rational homotopy groups | 2-stage space | MATHEMATICS | MATHEMATICS, APPLIED | DIMENSION | SPACES

55P62 | 55Q52 | rational cohomology groups | Hilali conjecture | rational homotopy groups | 2-stage space | MATHEMATICS | MATHEMATICS, APPLIED | DIMENSION | SPACES

Journal Article

Arabian Journal of Mathematics, ISSN 2193-5343, 3/2018, Volume 7, Issue 1, pp. 39 - 47

Let X be a simply connected CW-complex of finite type and $${\mathbb {K}}$$ K an arbitrary field. In this paper, we use the Eilenberg–Moore spectral sequence...

55P62 | Mathematics, general | Mathematics | 55T20 | 55M30 | Lower bounds | Invariants

55P62 | Mathematics, general | Mathematics | 55T20 | 55M30 | Lower bounds | Invariants

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

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

BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, ISSN 1370-1444, 07/2015, Volume 22, Issue 3, pp. 455 - 469

We give simple upper bounds-for rational sectional category and use them to compute invariants of the type of Farber's topological complexity of rational...

MATHEMATICS | topological complexity | sectional category | Rational homotopy | Homotopy theory | Analysis | Invariants | Mappings (Mathematics) | 55P62 | 55M30

MATHEMATICS | topological complexity | sectional category | Rational homotopy | Homotopy theory | Analysis | Invariants | Mappings (Mathematics) | 55P62 | 55M30

Journal Article

Osaka Journal of Mathematics, ISSN 0030-6126, 06/2010, Volume 47, Issue 2, pp. 439 - 460

The based loop space homology of a special family of homogeneous spaces, flag manifolds of connected compact Lie groups is studied. First, the rational...

MATHEMATICS | 55P62 | 57T35 | 57T20 | 55P35

MATHEMATICS | 55P62 | 57T35 | 57T20 | 55P35

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

EXISTENCE | MATHEMATICS | Clifford-Klein form | transgression | PROPER ACTIONS | HOMOGENEOUS SPACES | pure Sullivan algebra | relative Lie algebra cohomology

Journal Article

Boletín de la Sociedad Matemática Mexicana, ISSN 1405-213X, 10/2017, Volume 23, Issue 2, pp. 847 - 851

Let Aut(p) denote the space of all self-fibre homotopy equivalences of a principal G-bundle $$p: E\rightarrow X$$ p : E → X of simply connected CW complexes...

Fibre homotopy equivalence | Sullivan minimal model | Derivation | 55P62 | Mathematics, general | Mathematics | Samelson–Lie algebra | 55P10

Fibre homotopy equivalence | Sullivan minimal model | Derivation | 55P62 | Mathematics, general | Mathematics | Samelson–Lie algebra | 55P10

Journal Article

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