Autour de la cohomologie de Bott-Chern

Abstract

The goal of the memoir is to develop a new cohomology theory which encompasses De Rham and Dolbeault cohomology as well as Deligne Beilinson cohomology, in the context of general complex analytic manifolds. The special case of the Iwasawa manifold is investigated as a typical example of what occurs in the non Kähler case. Elementary applications to the Kodaira-Spencer deformation theory and to the calculation of Chern classes are given.

arXiv comment28 pages, part of PhD project

Cited by in corpus (37)

• The cohomologies of the Iwasawa manifold and of its small deformations
• Rational curves and special metrics on twistor spaces
• Canonical metrics on holomorphic Courant algebroids
• On Bott-Chern cohomology and formality
• Chern classes in Deligne cohomology for coherent analytic sheaves
• Note on Dolbeault cohomology and Hodge structures up to bimeromorphisms
• Inequalities à la Frölicher and cohomological decompositions
• On small deformations of balanced manifolds
• A parabolic flow of balanced metrics
• Cohomologies of certain orbifolds
• Hodge theory for twisted differentials
• The Frolicher-type inequalities of foliations
• Deformations of Dolbeault cohomology classes
• Cohomological aspects of non-Kähler manifolds
• On the deformed Bott-Chern cohomology
• Generalized Cohomologies and Supersymmetry
• Dolbeault cohomology of compact complex manifolds with an action of a complex Lie group
• On Bott-Chern and Aeppli cohomologies of almost complex manifolds and related spaces of harmonic forms
• Intersection theory and Chern classes in Bott-Chern cohomology
• Localization of Bott-Chern classes and Hermitian residues
• Several special complex structures and their deformation properties
• On the Bott-Chern and Aeppli cohomology
• Aeppli and Bott-Chern cohomology for bi-generalized Hermitian manifolds and $d^{\prime }{d}^{\prime \prime }$-lemma
• Bott-Chern cohomology and q-complete domains
• Coherent sheaves, superconnections, and RRG
• Remarks on Dolbeault cohomology of Oeljeklaus-Toma manifolds and Hodge theory
• Deformation of Kähler manifolds
• Bott-Chern Laplacian on almost Hermitian manifolds
• Extensions of $\overline{\partial }$-closed forms on compact generalized Hermitian manifolds
• Blow-up formulae for twisted cohomologies with supports
• Cohomologies on almost complex manifolds and the $\partial \bar{\partial }$-lemma
• On tangential cohomology attached to a function on complex foliations
• The jumping phenomenon of the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups
• Some Morse-type inequalities for symplectic manifolds
• Coeffective basic cohomologies of $K$--contact and Sasakian manifolds
• Bott-Chern-Aeppli, Dolbeault and Frolicher on Compact Complex 3-folds
• On the Bott-Chern cohomology and balanced Hermitian nilmanifolds