Dolbeault homotopy theory and compact nilmanifolds

L. Cordero; M. Fernández; A. Gray; L. Ugarte

Banach Center Publications (1998)

  • Volume: 45, Issue: 1, page 137-154
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Cordero, L., et al. "Dolbeault homotopy theory and compact nilmanifolds." Banach Center Publications 45.1 (1998): 137-154. <http://eudml.org/doc/208898>.

@article{Cordero1998,
abstract = {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.},
author = {Cordero, L., Fernández, M., Gray, A., Ugarte, L.},
journal = {Banach Center Publications},
keywords = {nilmanifolds; cohomology Frölicher spectral sequence; cohomotopy Frölicher spectral sequence; nilpotent complex structure},
language = {eng},
number = {1},
pages = {137-154},
title = {Dolbeault homotopy theory and compact nilmanifolds},
url = {http://eudml.org/doc/208898},
volume = {45},
year = {1998},
}

TY - JOUR
AU - Cordero, L.
AU - Fernández, M.
AU - Gray, A.
AU - Ugarte, L.
TI - Dolbeault homotopy theory and compact nilmanifolds
JO - Banach Center Publications
PY - 1998
VL - 45
IS - 1
SP - 137
EP - 154
AB - 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.
LA - eng
KW - nilmanifolds; cohomology Frölicher spectral sequence; cohomotopy Frölicher spectral sequence; nilpotent complex structure
UR - http://eudml.org/doc/208898
ER -

References

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