WebAug 25, 2005 · 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 … WebIn 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 …
Organized Collapse: An Introduction to Discrete Morse Theory
WebMay 26, 2012 · The overall output of the computations is a list of persistence pairs of the form (birth, death). This information can be visualized in different ways. ... Basic definitions of discrete Morse theory: (a) the cell graph G C, the node labels indicate the dimension of the represented cells; ... WebAt other times, critical points “die". Generically, critical points are born and die in pairs. Such events are isolated since the critical points of a Morse function are separated; we call … immunohistochemistry ihc handbook
(PDF) Birth and death in discrete Morse theory
WebAug 31, 2008 · 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 … WebThe central result presented here is an extension of discrete Morse theory to filtered cell com-plexes. This result is from [27] and we cover it here in Chapter4. Discrete Morse theory was originally developed by Robin Forman [13] for regular CW com-plexes. The basic idea of this theory is to define a pairing Von some of the cells of a given com- WebIn 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 … immunohistochemistry process