Forman's discrete Morse theory is studied from an algebraic viewpoint. Analogous to independent work of Emil Sköldberg, the authors show that this theory can be aplied to chain complexes of free modules over a ring and provide four applications of this theory.

Table of Contents

• Introduction
• Algebraic discrete Morse theory
• Resolution of the residue field in the commutative case
• Resolution of the residue field in the non-commutative case
• Application to acyclic Hochschild complex
• Minimal (cellular) resolutions for (\(p\)-) Borel fixed ideals
• Appendix A. The bar and the Hochschild complex
• Appendix B. Proofs for algebraic discrete Morse theory
• Bibliography
• Index