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)
“It isn’t that you subordinate your ideas to the force of the facts in autobiography but that you construct a sequence of stories to bind up the facts with a persuasive hypothesis that unravels your history’s meaning.”
—Philip Roth (b. 1933)