Constructive Homological Algebra and Applications

TL;DR

This paper provides a detailed exposition of constructive homological algebra using the Basic Perturbation Lemma, demonstrating its applications in commutative algebra and algebraic topology.

Contribution

It introduces a constructive approach to homological algebra, enabling effective computations in algebraic topology and commutative algebra.

Findings

Application of the Basic Perturbation Lemma to constructiveness

Development of effective spectral sequences

Use of Koszul complexes in computational algebra

Abstract

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 (standard Homological Algebra is not constructive) and how this technology can be used in Commutative Algebra (Koszul complexes) and Algebraic Topology (effective versions of spectral sequences).