Homology Spectral Sequence
Similarly to the cohomology spectral sequence, there is one for homology:
where the notations are dual to the ones above.
It is actually a special case of a more general spectral sequence, namely the Serre spectral sequence for fibrations of simplicial sets. If f is a fibration of simplicial sets (a Kan fibration), such that π1(B) the first homotopy group of the simplicial set B, vanishes, there is a spectral sequence exactly as above. (Applying the functor which associates to any topological space its simplices to a fibration of topological spaces, one recovers the above sequence).
Read more about this topic: Serre Spectral Sequence
Famous quotes containing the words spectral and/or sequence:
“How does one kill fear, I wonder? How do you shoot a spectre through the heart, slash off its spectral head, take it by its spectral throat?”
—Joseph Conrad (1857–1924)
“We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.”
—E.M. (Edward Morgan)