Hurewicz spectral sequence for homology

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For any connected space X and ring R, we describe a first-quadrant spectral sequence converging to H. (X; R), whose E2-term depends only on the homotopy groups of X and the action of the primary homotopy operations on them. We show that (for simply connected X) the E2-term vanishes below a line of slope 1/2; computing part of the E2-term just above this line, we find a certain periodicity, which shows, in particular, that this vanishing line is best possible. We also show how the differentials in this spectral sequence can be used to compute certain Toda brackets.

Original languageEnglish
Pages (from-to)335-354
Number of pages20
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - Mar 1990
Externally publishedYes


  • Derived functors
  • Homology
  • Homotopy
  • Hurewicz homomorphism
  • Spectral sequences
  • π algebras

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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