Effective spectral systems relating Serre and Eilenberg–Moore spectral sequences. (January 2023)

• Record Type: Journal Article
• Authors: Miguel, Daniel; Guidolin, Andrea; Romero, Ana; Rubio, Julio
• Is Part Of: Journal of symbolic computation. Volume 114(2023)
• Page Start: 122
• Page End: 148
• Publication Date: 2023-01
• Subjects: Constructive Algebraic Topology -- Spectral systems -- Spectral sequences -- Effective homology; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.04.014
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Working in a simplicial and constructive context, a new spectral system is defined that relates Serre and Eilenberg–Moore spectral sequences associated to a principal simplicial fibration. The two Eilenberg–Moore spectral sequences (the one where the homology of the fiber is the output, and the other where the homology of the base is computed) are used in our construction. Explicit computer programs are developed, enhancing the Kenzo computer algebra tool to implement that spectral system.