Dolbeault homotopy theory and compact nilmanifolds

Volume 45 / 1998

L. Cordero, M. Fernández, A. Gray, L. Ugarte Banach Center Publications 45 (1998), 137-154 DOI: 10.4064/-45-1-137-154


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.


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

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