Computing spectral sequences

TL;DR

This paper introduces new programs for the Kenzo system that compute Serre and Eilenberg-Moore spectral sequences, including differentials, convergence, and filtrations, enhancing algebraic topology computations.

Contribution

The paper presents fully automated programs for computing spectral sequences and their properties within the Kenzo system, a significant advancement in computational algebraic topology.

Findings

Successfully computes spectral sequences for complex spaces

Determines convergence and filtration of spectral sequences

Enhances Kenzo with new computational capabilities

Abstract

In this paper, a set of programs enhancing the Kenzo system is presented. Kenzo is a Common Lisp program designed for computing in Algebraic Topology, in particular it allows the user to calculate homology and homotopy groups of complicated spaces. The new programs presented here entirely compute Serre and Eilenberg-Moore spectral sequences, in particular the groups and differential maps for arbitrary r. They also determine when the spectral sequence has converged and describe the filtration of the target homology groups induced by the spectral sequence.