# Constructive Homological Algebra and Applications

@article{Rubio2012ConstructiveHA, title={Constructive Homological Algebra and Applications}, author={Julio Rubio and Francis Sergeraert}, journal={arXiv: K-Theory and Homology}, year={2012} }

This text was written and used for a MAP Summer School at the University of Genova, August 28 to September 2, 2006. Available since then on the web site of the second author, it has been used and referenced by several colleagues working in Commutative Algebra and Algebraic Topology. To make safer such references, it was suggested to place it on the Arxiv repository.
It is a relatively detailed exposition of the use of the Basic Perturbation Lemma to make constructive Homological Algebra…

## 60 Citations

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The algorithm to get the effective homology of RX from the effective Homological Algebra of X can be considered the main result, and a combinatorial proof of the convergence of the Bousfield-Kan spectral sequence, based on the tapered nature of the stage E1.

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The constructive constraint of the BKSS leads to a significant reorganization of this rich material and, as it is most often the case, to a simpler and more explicit description.

### Integration of the Kenzo System within SageMath for New Algebraic Topology Computations

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This work makes it possible to communicate both computer algebra programs and the SageMath system with new capabilities in algebraic topology, such as the computation of homotopy groups and some kind of spectral sequences, dealing in particular with simplicial objects of an infinite nature.

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The Rubio–Sergeraert solution for Constructive Algebraic Topology is recalled and the concrete computer program Kenzo has been written down which precisely follows this method.

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