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.

28 pages, part of PhD project

Cited by in corpus (10)

• Hodge theory for twisted differentials
• Cohomological aspects of non-Kähler manifolds
• On Bott-Chern and Aeppli cohomologies of almost complex manifolds and related spaces of harmonic forms
• Coherent sheaves, superconnections, and RRG
• Bott-Chern Laplacian on almost Hermitian manifolds
• The jumping phenomenon of the dimensions of Bott-Chern cohomology groups and Aeppli cohomology groups
• On the Bott-Chern cohomology and balanced Hermitian nilmanifolds
• Coeffective basic cohomologies of $K$--contact and Sasakian manifolds
• On tangential cohomology attached to a function on complex foliations
• Some Morse-type inequalities for symplectic manifolds