A USER'S GUIDE TO DISCRETE MORSE THEORY
By Robin Forman. 2002
570 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/95e96a06d60204d271c3e144c3c2f915283f1168
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Citations in the corpus
- Topology of random simplicial complexes: a survey (2013, background): “Itisknownthatmanysimplicialcomplexesandposetsfoundinthe wildarehomotopyequivalenttowedgesofspheresofthesamedimension, andmanyresearchersintopologicalcombinatoricshavewonderedifthere isadeeperreasonwhy[21]. Isitpossiblethatasymptoticallyalmostall complexesarerelativelysimple, topologicallyspeaking? O”
- On the topology of random complexes built over stationary point processes. (2012, methodology): “The proof uses the discrete Morse theoretic approach (see [16]) similar to that of [22], Theorem 5.”
- Persistence Theory - From Quiver Representations to Data Analysis (2015, methodology): “Research Report arXiv:1312.3829 [math.AT]. 2013 (cit. on pp. 27, 62, 163, 165). [41] P. Bubenik and J. Scott. “Categorification of Persistent Homology”. In: Discrete and Computational Geometry (2014). To appear (cit.”
- On the independence complex of square grids (2006, unknown): “Theorem 1 ([5], Theorem 6.”
- Sharp vanishing thresholds for cohomology of random flag complexes (2012, background): “Simplicial complexes and posets in topological combinatorics are often homotopy equivalent to bouquets of d-spheres [14], [7], and proving this conjecture might provide a kind of measure-theoretic explanation of the seeming ubiquity of this phenomenon.”
- Minimal Resolutions Via Algebraic Discrete Morse Theory (2009, methodology): “In this chapter we derive an algebraic version of Discrete Morse theory as developed by Forman (see [13], [14]).”
- Combinatorial Morse theory and minimality of hyperplane arrangements (2007, methodology): “All the definitions and results in this section are taken from Forman [7; 8].”