Elsevier

Journal of Symbolic Computation

Volume 114, January–February 2023, Pages 122-148
Journal of Symbolic Computation

Effective spectral systems relating Serre and Eilenberg–Moore spectral sequences

https://doi.org/10.1016/j.jsc.2022.04.014Get rights and content
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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.

Keywords

Constructive Algebraic Topology
Spectral systems
Spectral sequences
Effective homology

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Supported by grants PID2020-115225RB-I00 and PID2020-116641GB-I00 funded by MCIN/AEI/10.13039/501100011033 and by the Wallenberg AI, Autonomous Systems and Software Program (WASP) funded by the Knut and Alice Wallenberg Foundation, grant KAW 2017.0450.