Serre Spectral Sequence. Motivation

[WWGD]

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?.

Thanks.

 

[WWGD]

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.


Thanks.