On the vanishing of Hochschild homology of locally complete intersections.
We consider almost-complex structures on whose total Chern classes differ from that of the standard (integrable) almost-complex structure. E. Thomas established the existence of many such structures. We show that if there exists an “exotic” integrable almost-complex structures, then the resulting complex manifold would have specific Hodge numbers which do not vanish. We also give a necessary condition for the nondegeneration of the Frölicher spectral sequence at the second level.
In this paper, we prove the existence of the theory of spectral sequences in the category of real semi normed spaces. Using this theory, we associate to any extension of discrete groups the Hochschild-Serre spectral sequence in bounded cohomology with coefficients. In addition, we give the explicit expression of the first and the second term of this spectral sequence without further hypothesis.
Beaucoup d’informations sur les groupes de cohomologie d’un espace sont obtenues à partir de la suite spectrale de Serre. Dans cet article on construit une suite spectrale de Serre dans le cas “non stable”. Cette suite spectrale “non stable” permet des calculs de groupes d’homotopie d’espaces fonctionnels.