Birth and death in discrete Morse theory. (January 2017)

• Record Type: Journal Article
• Authors: King, Henry; Knudson, Kevin; Mramor Kosta, Neža
• Is Part Of: Journal of symbolic computation. Volume 78(2017)
• Page Start: 41
• Page End: 60
• Publication Date: 2017-01
• Subjects: primary 57Q99 68U05 -- secondary 57R70 58E05 65D18 65R99; Discrete Morse theory -- Birth–death point; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.03.007
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Suppose M is a finite cell decomposition of a space X and that for 0 = t 0 < t 1 < ⋯ < t r = 1 we have a discrete Morse function F t i : M → R . In this paper, we study the births and deaths of critical cells for the functions F t i and present an algorithm for pairing the cells that occur in adjacent slices. We first study the case where the cell decomposition of X is the same for each t i, and then generalize to the case where they may differ. This has potential applications in topological data analysis, where one has function values at a sample of points in some region in space at several different times or at different levels in an object.