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Morse theory from an algebraic viewpoint


Author: Emil Sköldberg
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
Published electronically: August 25, 2005
MathSciNet review: 2171225
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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.


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Additional Information

Emil Sköldberg
Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland
Email: emil.skoldberg@nuigalway.ie

DOI: https://doi.org/10.1090/S0002-9947-05-04079-1
Received by editor(s): August 4, 2003
Published electronically: August 25, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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