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Nilpotent complex structures.

Luis A. Cordero, Marisa Fernández, Alfred Gray, Luis Ugarte (2001)

RACSAM

Este artículo presenta un panorama de algunos resultados recientes sobre estructuras complejas nilpotentes J definidas sobre nilvariedades compactas. Tratamos el problema de clasificación de nilvariedades compactas que admiten una tal J, el estudio de un modelo minimal de Dolbeault y su formalidad, y la construcción de estructuras complejas nilpotentes para las cuales la sucesión espectral de Frölicher no colapsa en el segundo término.

Noetherian loop spaces

Natàlia Castellana, Juan Crespo, Jérôme Scherer (2011)

Journal of the European Mathematical Society

The class of loop spaces of which the mod p cohomology is Noetherian is much larger than the class of p -compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg–Mac Lane spaces such as P and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space B X of such an object and prove it is as small as expected, that is, comparable to that of B P . We also show that B X differs basically from the classifying space of a p -compact group...

Non-abelian extensions of infinite-dimensional Lie groups

Karl-Hermann Neeb (2007)

Annales de l’institut Fourier

In this article we study non-abelian extensions of a Lie group G modeled on a locally convex space by a Lie group N . The equivalence classes of such extension are grouped into those corresponding to a class of so-called smooth outer actions S of G on N . If S is given, we show that the corresponding set Ext ( G , N ) S of extension classes is a principal homogeneous space of the locally smooth cohomology group H s s 2 ( G , Z ( N ) ) S . To each S a locally smooth obstruction class χ ( S ) in a suitably defined cohomology group H s s 3 ( G , Z ( N ) ) S is defined....

Non-degenerescence of some spectral sequences

K. S. Sarkaria (1984)

Annales de l'institut Fourier

Each Lie algebra of vector fields (e.g. those which are tangent to a foliation) of a smooth manifold M définies, in a natural way, a spectral sequence E k ( ) which converges to the de Rham cohomology of M in a finite number of steps. We prove e.g. that for all k 0 there exists a foliated compact manifold with E k ( ) infinite dimensional.

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