Autour de la cohomologie de Bott-Chern

TL;DR

This paper introduces a new cohomology theory for complex manifolds that unifies several existing theories and explores its properties through examples and applications.

Contribution

It develops a comprehensive cohomology framework that generalizes De Rham, Dolbeault, and Deligne Beilinson cohomologies for complex manifolds.

Findings

Unified cohomology theory encompassing multiple existing theories

Application to Iwasawa manifold illustrating non Kähler cases

Elementary applications to deformation theory and Chern classes

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 K\"ahler case. Elementary applications to the Kodaira-Spencer deformation theory and to the calculation of Chern classes are given.