In this paper we study the degeneration of both the cohomology and the cohomotopy Frölicher spectral sequences in a special class of complex manifolds, namely the class of compact nilmanifolds endowed with a nilpotent complex structure. Whereas the cohomotopy spectral sequence is always degenerate for such a manifold, there exist many nilpotent complex structures on compact nilmanifolds for which the classical Frölicher spectral sequence does not collapse even at the second term.
@article{bwmeta1.element.bwnjournal-article-bcpv45i1p137bwm,
author = {Cordero, L. and Fern\'andez, M. and Gray, A. and Ugarte, L.},
title = {Dolbeault homotopy theory and compact nilmanifolds},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {137-154},
zbl = {0943.32015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p137bwm}
}
Cordero, L.; Fernández, M.; Gray, A.; Ugarte, L. Dolbeault homotopy theory and compact nilmanifolds. Banach Center Publications, Tome 43 (1998) pp. 137-154. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p137bwm/
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