Morse theory from an algebraic viewpoint

Abstract

Forman's discrete Morse theory is studied from an algebraic viewpoint,and we show how this theory can be extended to chain complexes ofmodules over arbitrary rings. As applications we compute the homologiesof a certain family of nilpotent Lie algebras, and show how the algebraicMorse theory can be used to derive the classical Anick resolutionas well as a new two-sided Anick resolution.