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Serre Spectral Sequence. Motivation

  1. Feb 13, 2008 #1


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    Hi, everyone. I don't know if this is the right forum, here it goes:

    I have been reading on Serre's spectral sequence (Wiki, Hatcher). I understand the general goal, but I don't get well the process:

    how does a fibration F->E->B

    give rise to a spectral sequence?.

  2. jcsd
  3. Feb 13, 2008 #2


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    I guess I should be less impulsive in my posting: I just remembered that the base

    B is assumed a CW-complex, and that we consider the fiber of the n-skeleton,

    and this fiber somehow has the structure of a filtered chain complex. we somehow

    define in this filtered complex, a differential. Then we just have a filtered chain complex,

    and we follow the recipe for it .Still, the details are fuzzy.

    Also: what are the general ingredients for a spectral sequence?. We start with

    a sheet E_ro (ro=0,1,2, usually, ABAIK---Asbestos I know), then the next sheet

    is isomorphic to the homology of E_ro, and we then go on, until the sheets converge

    (we assume the sheets are non-zero only in the first quadrant, so that we run out

    of groups as we approach the quadrants.)

    Anyway, I would appreciate some comments, both on the Serre spectral, and

    in general for spectral sequences.

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