Birth and death in discrete Morse theory

Henry King; Kevin Knudson; Neza Mramor

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arXiv · 0808.0051

Birth and death in discrete Morse theory

Henry King·Kevin Knudson·Neza Mramor

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Abstract

Suppose $M$ is a finite simplicial complex and that for $0=t_0,t_1,...,t_r=1$ we have a discrete Morse function $F_{t_i}:M\to \zr$. 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 triangulation of $M$ is the same for each $t_i$, and then generalize to the case where the triangulations may differ. This has potential applications in data imaging, 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.

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Henry King, Kevin Knudson, Neza Mramor. 2008-08-01. Birth and death in discrete Morse theory. https://arxiv.org/abs/0808.0051

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