Memoirs of the American Mathematical Society 2009; 74 pp; softcover Volume: 197 ISBN10: 0821842579 ISBN13: 9780821842577 List Price: US$62 Individual Members: US$37.20 Institutional Members: US$49.60 Order Code: MEMO/197/923
 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 noncommutative 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
