Computing spectral sequences

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. Key words: Symbolic Computation, Spectral Sequences, Serre Spectral Sequence, Eilenberg-Moore Spectral Sequence, Constructive Algebraic Topol...

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Ana Romero, Julio Rubio, Francis Sergeraert
• Keywords: CORR 2006, Education, Effective Homology, Eilenberg-moore Spectral Sequence, Spectral Sequence