nLab Eilenberg–Moore spectral sequence

Idea

The Eilenberg-Moore spectral sequence is a spectral sequence for the singular homology of product topological spaces which generalizes the Künneth theorem in two ways

1. it applies without assumption on vanishing of Tor-groups;

2. it generalizes from product topological spaces to fiber products of fibrations and to products over group actions.

References

Original articles:

• Larry Smith, Homological Algebra and the Eilenberg-Moore Spectral Sequence, Transactions of the American Mathematical Society, Vol. 129, No. 1, (1967) (jstor:1994364)

• Larry Smith, On the construction of the Eilenberg-Moore spectral sequence, Bull. Amer. Math. Soc. 75 (1969), 873-878 (euclid:bams/1183530666)

• Atsushi Yamaguchi, Note on the Eilenberg-Moore spetral sequence, Publ RIMS, Ykoto Univ. 22 (1986) (pdf)

Textbook accounts include

• Alan Hatcher, Spectral sequences in algebraic topology III: The Eilenberg-Moore spectral sequence (pdf)