Reference for the construction of the Leray spectral sequence from filtration

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So far I have found only two possible constructions of the Leray spectral sequence for a continuous map $f : X to Y$ between topological spaces with CW-complex structures: one through Cech complexes, and the other one more categorical through Grothendieck spectral sequences.



I would like to construct this spectral sequence directly by hand from the filtration induced by the CW-structure of $Y$, but haven't found any reference about it.



May I emphasise that I'm looking for a construction of the Leray spectral sequence (for continuous maps which are not necessarily filtrations, and not of the Leray-Serre spectral sequence (where direct constructions can be found in many places).



Does someone have an idea ? Thanks !







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    up vote
    1
    down vote

    favorite












    So far I have found only two possible constructions of the Leray spectral sequence for a continuous map $f : X to Y$ between topological spaces with CW-complex structures: one through Cech complexes, and the other one more categorical through Grothendieck spectral sequences.



    I would like to construct this spectral sequence directly by hand from the filtration induced by the CW-structure of $Y$, but haven't found any reference about it.



    May I emphasise that I'm looking for a construction of the Leray spectral sequence (for continuous maps which are not necessarily filtrations, and not of the Leray-Serre spectral sequence (where direct constructions can be found in many places).



    Does someone have an idea ? Thanks !







    share|cite|improve this question






















      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      So far I have found only two possible constructions of the Leray spectral sequence for a continuous map $f : X to Y$ between topological spaces with CW-complex structures: one through Cech complexes, and the other one more categorical through Grothendieck spectral sequences.



      I would like to construct this spectral sequence directly by hand from the filtration induced by the CW-structure of $Y$, but haven't found any reference about it.



      May I emphasise that I'm looking for a construction of the Leray spectral sequence (for continuous maps which are not necessarily filtrations, and not of the Leray-Serre spectral sequence (where direct constructions can be found in many places).



      Does someone have an idea ? Thanks !







      share|cite|improve this question












      So far I have found only two possible constructions of the Leray spectral sequence for a continuous map $f : X to Y$ between topological spaces with CW-complex structures: one through Cech complexes, and the other one more categorical through Grothendieck spectral sequences.



      I would like to construct this spectral sequence directly by hand from the filtration induced by the CW-structure of $Y$, but haven't found any reference about it.



      May I emphasise that I'm looking for a construction of the Leray spectral sequence (for continuous maps which are not necessarily filtrations, and not of the Leray-Serre spectral sequence (where direct constructions can be found in many places).



      Does someone have an idea ? Thanks !









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 25 at 10:54









      BrianT

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