Annals of Global Analysis and Geometry, ISSN 0232-704X, 12/2017, Volume 52, Issue 4, pp. 363 - 411

We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott–Chern cohomology...

53C30 | Dolbeault cohomology | Solvmanifolds | Theoretical, Mathematical and Computational Physics | 53C55 | 53D05 | Mathematics | Geometry | 22E25 | 57T15 | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Invariant complex structure | Group Theory and Generalizations | Bott–Chern cohomology | LOCAL SYSTEMS | Bott-Chern cohomology | HODGE THEORY | KAHLER MANIFOLDS | MINIMAL MODELS | COMPACT NILMANIFOLDS | LIE-ALGEBRAS | MATHEMATICS | FROLICHER SPECTRAL SEQUENCE | DEFORMATIONS | Parallel processing | Deformation | Vector spaces | Quotients | Lie groups

53C30 | Dolbeault cohomology | Solvmanifolds | Theoretical, Mathematical and Computational Physics | 53C55 | 53D05 | Mathematics | Geometry | 22E25 | 57T15 | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Invariant complex structure | Group Theory and Generalizations | Bott–Chern cohomology | LOCAL SYSTEMS | Bott-Chern cohomology | HODGE THEORY | KAHLER MANIFOLDS | MINIMAL MODELS | COMPACT NILMANIFOLDS | LIE-ALGEBRAS | MATHEMATICS | FROLICHER SPECTRAL SEQUENCE | DEFORMATIONS | Parallel processing | Deformation | Vector spaces | Quotients | Lie groups

Journal Article

The Journal of geometric analysis, ISSN 1559-002X, 2019, Volume 30, Issue 1, pp. 493 - 510

We view Dolbeault-Morse-Novikov cohomology H eta p,q(X) as the cohomology of the sheaf Omega X,eta p of eta-holomorphic p-forms and give several bimeromorphic invariants...

Bimeromorphic | Sheaf of eta-holomorphic functions | Blow-up formula | Stability | Leray-Hirsch theorem | eta-hodge number | BLOW-UPS | Dolbeault-Morse-Novikov cohomology | MATHEMATICS | Weight theta-sheaf | theta-betti number | DOLBEAULT COHOMOLOGY | Morse-Novikov cohomology

Bimeromorphic | Sheaf of eta-holomorphic functions | Blow-up formula | Stability | Leray-Hirsch theorem | eta-hodge number | BLOW-UPS | Dolbeault-Morse-Novikov cohomology | MATHEMATICS | Weight theta-sheaf | theta-betti number | DOLBEAULT COHOMOLOGY | Morse-Novikov cohomology

Journal Article

International journal of mathematics, ISSN 1793-6519, 2014, Volume 25, Issue 6, pp. 1450057 - 1-1450057-24

The Bott–Chern cohomology of six-dimensional nilmanifolds endowed with invariant complex structure is studied with special attention to the cases when balanced or strongly Gauduchon Hermitian metrics exist...

Bott-chern cohomology | Holomorphic deformation | Complex structure | Nilmanifold | MATHEMATICS | SMALL DEFORMATIONS | complex structure | DOLBEAULT-COHOMOLOGY | Bott-Chern cohomology | holomorphic deformation | STABILITY | MANIFOLDS | COMPLEX STRUCTURES | GEOMETRY | Balancing | Deformation | Mathematical analysis | Supergravity | Invariants

Bott-chern cohomology | Holomorphic deformation | Complex structure | Nilmanifold | MATHEMATICS | SMALL DEFORMATIONS | complex structure | DOLBEAULT-COHOMOLOGY | Bott-Chern cohomology | holomorphic deformation | STABILITY | MANIFOLDS | COMPLEX STRUCTURES | GEOMETRY | Balancing | Deformation | Mathematical analysis | Supergravity | Invariants

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 07/2015, Volume 93, pp. 52 - 61

We study a geometric notion related to formality for Bott–Chern cohomology on complex manifolds.

Complex manifold | Hermitian metric | Cohomology | Formality | Bott–Chern cohomology | Bott-Chern cohomology | MATHEMATICS | COMPLEX | SOLVMANIFOLDS | MANIFOLDS | DOLBEAULT COHOMOLOGY | PHYSICS, MATHEMATICAL | Bott-Chem cohomology | HOMOTOPY THEORY

Complex manifold | Hermitian metric | Cohomology | Formality | Bott–Chern cohomology | Bott-Chern cohomology | MATHEMATICS | COMPLEX | SOLVMANIFOLDS | MANIFOLDS | DOLBEAULT COHOMOLOGY | PHYSICS, MATHEMATICAL | Bott-Chem cohomology | HOMOTOPY THEORY

Journal Article

ALGEBRAIC GEOMETRY, ISSN 2313-1691, 07/2019, Volume 6, Issue 4, pp. 384 - 409

We define monodromy maps for the tropical Dolbeault cohomology of algebraic varieties over non-Archimedean fields...

MATHEMATICS | tropical Dolbeault cohomology | monodromy map

MATHEMATICS | tropical Dolbeault cohomology | monodromy map

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 10/2018, Volume 290, Issue 1-2, pp. 521 - 537

Journal Article

Quarterly Journal of Mathematics, ISSN 0033-5606, 2017, Volume 68, Issue 3, pp. 705 - 728

We study quaternionic Bott-Chern cohomology on compact hypercomplex manifolds and adapt some results from complex geometry to the quaternionic setting...

MATHEMATICS | INVARIANT COMPLEX STRUCTURE | BUNDLES | KAHLER | TORSION | MANIFOLDS | DOLBEAULT COHOMOLOGY | COMPACT NILMANIFOLDS | SURFACES | GEOMETRY | Mathematics - Differential Geometry

MATHEMATICS | INVARIANT COMPLEX STRUCTURE | BUNDLES | KAHLER | TORSION | MANIFOLDS | DOLBEAULT COHOMOLOGY | COMPACT NILMANIFOLDS | SURFACES | GEOMETRY | Mathematics - Differential Geometry

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2018, Volume 70, Issue 1, pp. 409 - 422

.... The L-valued cohomology of M is called Morse-Novikov cohomology; it was conjectured that (just as it happens for Kahler manifolds...

Dolbeault cohomology | Vaisman manifold | Vanishing | Morse–Novikov cohomology | locally conformally Kähler manifold | Potential | Bott–Chern cohomology | MATHEMATICS | Bott-Chern cohomology | locally conformally Kahler manifold | vanishing | CONFORMALLY KAHLER-MANIFOLDS | potential | Morse-Novikov cohomology | LOCAL COHOMOLOGY | SURFACES

Dolbeault cohomology | Vaisman manifold | Vanishing | Morse–Novikov cohomology | locally conformally Kähler manifold | Potential | Bott–Chern cohomology | MATHEMATICS | Bott-Chern cohomology | locally conformally Kahler manifold | vanishing | CONFORMALLY KAHLER-MANIFOLDS | potential | Morse-Novikov cohomology | LOCAL COHOMOLOGY | SURFACES

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 09/2013, Volume 71, pp. 117 - 126

We study the Bott–Chern cohomology of complex orbifolds obtained as a quotient of a compact complex manifold by a finite group of biholomorphisms.

[formula omitted]-lemma | Orbifolds | Bott–Chern cohomology | Bott-Chern cohomology | lemma | partial derivative partial derivative-lemma | HOLONOMY SPIN | MATHEMATICS, APPLIED | COMPACT 8-MANIFOLDS | MANIFOLDS | PHYSICS, MATHEMATICAL | DOLBEAULT | Mathematics - Differential Geometry

[formula omitted]-lemma | Orbifolds | Bott–Chern cohomology | Bott-Chern cohomology | lemma | partial derivative partial derivative-lemma | HOLONOMY SPIN | MATHEMATICS, APPLIED | COMPACT 8-MANIFOLDS | MANIFOLDS | PHYSICS, MATHEMATICAL | DOLBEAULT | Mathematics - Differential Geometry

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 2/2013, Volume 273, Issue 1, pp. 437 - 447

... such that N are nilpotent Lie groups with left-invariant complex structures. We compute the Dolbeault cohomology of direct sums of holomorphic line bundles over G/Γ...

22E25 | 53C30 | Dolbeault cohomology | Solvmanifold | 53C55 | Mathematics, general | Invariant complex structure | Holomorphic line bundle | Mathematics | MATHEMATICS | COMPACT NILMANIFOLDS | Methods | Algebra

22E25 | 53C30 | Dolbeault cohomology | Solvmanifold | 53C55 | Mathematics, general | Invariant complex structure | Holomorphic line bundle | Mathematics | MATHEMATICS | COMPACT NILMANIFOLDS | Methods | Algebra

Journal Article

Annals of Global Analysis and Geometry, ISSN 0232-704X, 3/2017, Volume 51, Issue 2, pp. 155 - 177

.... We also give explicit finite-dimensional cochain complexes which computes the holomorphic Poisson cohomology of nilmanifolds and solvmanifolds.

Primary: 17B30 | Dolbeault cohomology | Holomorphic Poisson cohomology | Solvmanifold | Theoretical, Mathematical and Computational Physics | Mathematics | 32G05 | 32M10 | 58H15 | 53D18 | Geometry | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Deformation of generalized complex structure | Group Theory and Generalizations | MATHEMATICS | KAHLER | SOLVABLE LIE-GROUPS | COMPLEX STRUCTURES | COMPACT NILMANIFOLDS | Studies | Algebra | Homology | Deformation | Structural stability | Mathematical analysis | Smoothness

Primary: 17B30 | Dolbeault cohomology | Holomorphic Poisson cohomology | Solvmanifold | Theoretical, Mathematical and Computational Physics | Mathematics | 32G05 | 32M10 | 58H15 | 53D18 | Geometry | Statistics for Business/Economics/Mathematical Finance/Insurance | Analysis | Deformation of generalized complex structure | Group Theory and Generalizations | MATHEMATICS | KAHLER | SOLVABLE LIE-GROUPS | COMPLEX STRUCTURES | COMPACT NILMANIFOLDS | Studies | Algebra | Homology | Deformation | Structural stability | Mathematical analysis | Smoothness

Journal Article

Mathematical Research Letters, ISSN 1073-2780, 2014, Volume 21, Issue 4, pp. 781 - 805

...". By this result, we construct an explicit finite-dimensional cochain complex which compute the cohomology H*(G/Gamma, E...

De Rham cohomology | Dolbeault cohomology | Local system | Solvmanifold | Lie algebra cohomology | MATHEMATICS | solvmanifold | LIE-GROUPS | de Rham cohomology | local system | POLYNOMIAL STRUCTURES

De Rham cohomology | Dolbeault cohomology | Local system | Solvmanifold | Lie algebra cohomology | MATHEMATICS | solvmanifold | LIE-GROUPS | de Rham cohomology | local system | POLYNOMIAL STRUCTURES

Journal Article

Differential Geometry and its Applications, ISSN 0926-2245, 02/2016, Volume 44, pp. 144 - 160

.... As a basic fact, we establish that on such manifolds, the Dolbeault cohomology with coefficients in holomorphic polyvector fields is isomorphic to the cohomology of invariant forms with coefficients...

Abelian complex structure | Spectral sequence | Holomorphic Poisson structure | Nilmanifold | MATHEMATICS, APPLIED | DOLBEAULT-COHOMOLOGY | COMPACT NILMANIFOLDS | MATHEMATICS | ALGEBRAS | DEFORMATIONS | MANIFOLDS | GENERALIZED COMPLEX STRUCTURES | GEOMETRY

Abelian complex structure | Spectral sequence | Holomorphic Poisson structure | Nilmanifold | MATHEMATICS, APPLIED | DOLBEAULT-COHOMOLOGY | COMPACT NILMANIFOLDS | MATHEMATICS | ALGEBRAS | DEFORMATIONS | MANIFOLDS | GENERALIZED COMPLEX STRUCTURES | GEOMETRY

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 8/2013, Volume 274, Issue 3, pp. 1165 - 1176

...Math. Z. (2013) 274:1165–1176 DOI 10.1007/s00209-012-1111-z Mathematische Zeitschrift On the Hausdorff property of some Dolbeault cohomology groups Christine...

32C35 | Dolbeault cohomology | Separation | Mathematics, general | Mathematics | Duality | 32C37 | MATHEMATICS | SERRE DUALITY | OPERATOR | REGULARITY | MANIFOLDS

32C35 | Dolbeault cohomology | Separation | Mathematics, general | Mathematics | Duality | 32C37 | MATHEMATICS | SERRE DUALITY | OPERATOR | REGULARITY | MANIFOLDS

Journal Article

The Journal of Geometric Analysis, ISSN 1050-6926, 1/2017, Volume 27, Issue 1, pp. 142 - 161

We study generalized complex cohomologies of generalized complex structures constructed from certain symplectic fiber bundles over complex manifolds...

Deformation | 32G07 | Mathematics | Cohomology | 53D18 | Abstract Harmonic Analysis | Generalized complex | Fourier Analysis | 57T15 | Convex and Discrete Geometry | Nilmanifold | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | DOLBEAULT-COHOMOLOGY | HODGE THEORY | DECOMPOSITION | Mathematics - Differential Geometry

Deformation | 32G07 | Mathematics | Cohomology | 53D18 | Abstract Harmonic Analysis | Generalized complex | Fourier Analysis | 57T15 | Convex and Discrete Geometry | Nilmanifold | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | MATHEMATICS | DOLBEAULT-COHOMOLOGY | HODGE THEORY | DECOMPOSITION | Mathematics - Differential Geometry

Journal Article

中国科学：数学英文版, ISSN 1674-7283, 2017, Volume 60, Issue 6, pp. 949 - 962

The main purpose of this paper is to generalize the celebrated L2 extension theorem of Ohsawa and Takegoshi in several directions： The holomorphic sections to...

plurisubharmonic function | compact Kähler manifold | Dolbeault cohomology | coherent sheaf cohomology | singular hermitian metric | multiplier ideal sheaf | Ohsawa-Takegoshi extension theorem | estimates | MATHEMATICS | L-2 estimates | MATHEMATICS, APPLIED | compact Kahler manifold

plurisubharmonic function | compact Kähler manifold | Dolbeault cohomology | coherent sheaf cohomology | singular hermitian metric | multiplier ideal sheaf | Ohsawa-Takegoshi extension theorem | estimates | MATHEMATICS | L-2 estimates | MATHEMATICS, APPLIED | compact Kahler manifold

Journal Article

Annali della Scuola normale superiore di Pisa - Classe di scienze, ISSN 0391-173X, 2011, Volume 10, Issue 4, pp. 801 - 818

...] on the de Rham cohomology of a compact solvmanifold, i.e., of a quotient of a connected and simply connected solvable Lie group G by a lattice Gamma...

SPLITTINGS | MATHEMATICS | DOLBEAULT-COHOMOLOGY | SOLVABLE LIE-GROUPS | HOMOGENEOUS SPACES | MANIFOLDS | NILMANIFOLDS

SPLITTINGS | MATHEMATICS | DOLBEAULT-COHOMOLOGY | SOLVABLE LIE-GROUPS | HOMOGENEOUS SPACES | MANIFOLDS | NILMANIFOLDS

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 2017, Volume 145, Issue 1, pp. 273 - 285

We introduce a "qualitative property" for Bott-Chern cohomology of complex non-Kahler manifolds, which is motivated in view of the study of the algebraic structure of Bott-Chern cohomology...

Complex manifold | Bott-Chern cohomology | Non-Kähler geometry | Lemma | Aeppli cohomology | non-Kahler geometry | MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX | HODGE THEORY | partial derivative partial derivative-Lemma | DOLBEAULT | HOMOTOPY THEORY

Complex manifold | Bott-Chern cohomology | Non-Kähler geometry | Lemma | Aeppli cohomology | non-Kahler geometry | MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX | HODGE THEORY | partial derivative partial derivative-Lemma | DOLBEAULT | HOMOTOPY THEORY

Journal Article

Journal of Geometric Analysis, ISSN 1050-6926, 7/2013, Volume 23, Issue 3, pp. 1355 - 1378

We prove that, for some classes of complex nilmanifolds, the Bott–Chern cohomology is completely determined by the Lie algebra associated with the nilmanifold with the induced complex structure...

Iwasawa manifold | Bott–Chern | Deformations | Solvmanifold | Mathematics | 53C15 | Cohomology | 32G05 | Abstract Harmonic Analysis | Fourier Analysis | 57T15 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Bott-Chern | MATHEMATICS | INVARIANT COMPLEX STRUCTURE | KAHLER MANIFOLDS | DOLBEAULT COHOMOLOGY | COMPACT NILMANIFOLDS | Algebra | Mathematics - Differential Geometry

Iwasawa manifold | Bott–Chern | Deformations | Solvmanifold | Mathematics | 53C15 | Cohomology | 32G05 | Abstract Harmonic Analysis | Fourier Analysis | 57T15 | Convex and Discrete Geometry | Global Analysis and Analysis on Manifolds | Differential Geometry | Dynamical Systems and Ergodic Theory | Bott-Chern | MATHEMATICS | INVARIANT COMPLEX STRUCTURE | KAHLER MANIFOLDS | DOLBEAULT COHOMOLOGY | COMPACT NILMANIFOLDS | Algebra | Mathematics - Differential Geometry

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 2009, Volume 1093, Issue 1, pp. 57 - 69

We study the (generalized Dolbeault) cohomology of generalized complex manifolds in 4 real dimensions...

Generalized complex structures | Dolbeault cohomology | COMPLEX MANIFOLDS | NUMERICAL ANALYSIS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SUPERGRAVITY | CALCULATION METHODS | QUANTUM FIELD THEORY | GAUGE INVARIANCE

Generalized complex structures | Dolbeault cohomology | COMPLEX MANIFOLDS | NUMERICAL ANALYSIS | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SUPERGRAVITY | CALCULATION METHODS | QUANTUM FIELD THEORY | GAUGE INVARIANCE

Conference Proceeding

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