Towards Optimality in Discrete Morse Theory through Chain Homotopies
نویسندگان
چکیده
Once a discrete Morse function has been defined on a finite cell complex, information about its homology can be deduced from its critical elements. The main objective of this paper is to define optimal discrete gradient vector fields on general finite cell complexes, where optimality entails having the least number of critical elements. Our approach is to consider this problem as a homology computation question for chain complexes endowed with extra algebraic nilpotent operator.
منابع مشابه
Homological optimality in Discrete Morse Theory through chain homotopies
0167-8655/$ see front matter 2012 Published by doi:10.1016/j.patrec.2012.01.014 ⇑ Corresponding author. E-mail address: [email protected] (H. Molina-Abril). Morse theory is a fundamental tool for analyzing the geometry and topology of smooth manifolds. This tool was translated by Forman to discrete structures such as cell complexes, by using discrete Morse functions or equivalently gradient vector f...
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تاریخ انتشار 2010