nLab Eilenberg–Moore spectral sequence

Contents

Context

Homological algebra

homological algebra

(also nonabelian homological algebra)

Introduction

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Schanuel's lemma

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:

  • 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

Last revised on January 12, 2021 at 15:38:38. See the history of this page for a list of all contributions to it.