nLab
Eilenberg–Moore spectral sequence

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Contents

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 include

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

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

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

Textbook accounts include

Revised on October 29, 2012 20:25:04 by Urs Schreiber (131.174.188.167)