Layra-chan
I don't suppose anyone knows why
spectral sequences are called such.
The best answer that my Algebraic Topology class could come up with was that the spectral sequence produces a total complex that is given as a direct sum of groups (via a filtration), somewhat like how a linear transformation is given as a sum of its eigenvalues times the projections to its eigenspaces. The reason is a bit of a stretch.
Apparently the prof. asked someone in the department who asked Serre and Borel, and neither Serre nor Borel knew the answer.
You can thank Jean Leray for the terminology, as well as the confusion. He created the term, but never published a reason for the name. To my knowledge the best explanation anyone has been able to offer is something along the lines of, "Since he was an analyst he may have viewed the data in each term of a spectral sequence as playing a role that the eigenvalues, revealed one at a time, have for an operator."
I believe that was the about the phrasing offered by John McCleary (and others).
Reply
