Spectral Sequences: Uses, Problems and Computations

Dr. Ana Romero (Universidad de La Rioja)

Abstract

Spectral Sequences are a useful tool in Algebraic Topology providing
information on homology and homotopy groups, but they are not real
algorithms except in some particular cases. On the contrary, the
effective homology method provides algorithms for the computation of
homology groups of complicated spaces, and in particular it allows to
determine the homology groups of some spaces related to the most
common spectral sequences. In this talk, we explain how the effective
homology technique can also be used to obtain, as a by-product, an
algorithm computing every component of the  corresponding  spectral
sequence. These methods have been concretely implemented as an
extension of the Kenzo computer program.