Morse theory from an algebraic viewpoint

By Emil Sköldberg. 2005

132 citations recorded by the source corpus.

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

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cf64b2cd3ec7ec3cdf7c593abab21107e43274cd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Bruno Benedetti
2. M. Joellenbeck
3. Volkmar Welker

In Geometry and Topology

1. Bruno Benedetti
2. M. Joellenbeck
3. Volkmar Welker

In Mathematical Physics

1. Bruno Benedetti
2. M. Joellenbeck
3. Volkmar Welker

Citations in the corpus

• Discrete Morse Theory for Manifolds with Boundary (2010, background): “Discrete Morse theory opens doors to computational geometry [24, 39, 41, 44] and to commutative algebra [3, 40, 68].”
• Minimal Resolutions Via Algebraic Discrete Morse Theory (2009, methodology): “Our applications require a slightly more general setting than the one covered in [22] therefore, we give a detailed exposition of the theory here and provide proofs in Appendix B.”