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Jun, 2019
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Spectral Sequences

Spectral sequences are one of the most effective computational tools in algebraic topology.

Spectral sequences are introduced by J. Leray. Leray’s spectral sequence was translated into the form suitable for algebraic topology by J.-P. Serre and served as a powerful tool in the developement of the early stage of algebraic topology. The reader is recommended to read McCleary’s [ McC99 ] .

The study of spectral sequences can be split into the following two parts.

  • general theory of exact couples and spectral sequences
  • constructions of spectral sequences motivated by topological problems and computations of (co)homology

References