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Towards optimality in discrete Morse Theory through chain homotopies

 

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Opened Access Towards optimality in discrete Morse Theory through chain homotopies
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Author: Real Jurado, Pedro
Molina Abril, Helena
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I
Date: 2010
Published in: Image-A : Applicable Mathematics in Image Engineering, 1 (1), 33-40
Document type: Article
Abstract: 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.
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URI: http://hdl.handle.net/11441/26196

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