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The higher Leray-Serre spectral sequence associated with a tower offibrations represents a generalization of the classical Leray-Serre spectralsequence of a fibration. In this work, we present algorithms to compute higherLeray-Serre spectral sequences leveraging the effective homology technique,which allows to perform computations involving chain complexes of infinite typeassociated with interesting objects in algebraic topology. In order to developthe programs, implemented as a new module for the Computer Algebra systemKenzo, we translated the original construction of the higher Leray-Serrespectral sequence in a simplicial framework and studied some of its fundamentalproperties.

Computing higher Leray-Serre spectral sequences of towers of fibrations