## Morse theory from an algebraic viewpoint

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- by Emil Sköldberg PDF
- Trans. Amer. Math. Soc.
**358**(2006), 115-129 Request permission

## Abstract:

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.## References

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## Additional Information

**Emil Sköldberg**- Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland
- Email: emil.skoldberg@nuigalway.ie
- Received by editor(s): August 4, 2003
- Published electronically: August 25, 2005
- © Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**358**(2006), 115-129 - MSC (2000): Primary 16E05; Secondary 16E40, 17B56
- DOI: https://doi.org/10.1090/S0002-9947-05-04079-1
- MathSciNet review: 2171225