Computing spectral sequences

  1. Julio Rubio García 2
  2. Francis Sergeraert 1
  3. Ana Romero Ibáñez
  1. 1 Joseph Fourier University

    Joseph Fourier University

    Grenoble, Francia

    GRID grid.9621.c

  2. 2 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Journal of symbolic computation

ISSN: 0747-7171

Year of publication: 2006

Volume: 41

Issue: 10

Pages: 1059-1079

Type: Article

Export: RIS
DOI: 10.1016/j.jsc.2006.06.002
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John McCleary insisted in his interesting textbook entitled ¿User¿s guide to spectral sequences¿ on the fact that the tool ¿spectral sequence¿ is not in the general situation an algorithm allowing its user to compute the looked-for homology groups. The present article explains how the notion of ¿Object with Effective Homology¿ on the contrary allows the user to recursively obtain all the components of the Serre and Eilenberg¿Moore spectral sequences, when the data are objects with effective homology. In particular the computability problem of the higher differentials is solved, the extension problem at abutment is also recursively solved. Furthermore, these methods have been concretely implemented as an extension of the Kenzo computer program. Two typical examples of spectral sequence computations are reported.