Effective Computation of Generalized Spectral Sequences

Abstract

In this paper, we present some algorithms and programs for computing generalized spectral sequences, a useful tool in Computational Algebraic Topology which provides topological information on spaces with generalized filtrations over a poset. Our programs have been implemented as a new module for the Kenzo system and solve the classical problems of spectral sequences which are differential maps and extensions. Moreover, combined with the use of effective homology and discrete vector fields, the programs make it possible to compute generalized spectral sequences of big spaces, sometimes of infinite type.