Results 11 to 20 of about 57,386 (206)
Discrete Morse Theory and Extended L2 Homology [PDF]
Journal of Functional Analysis, 1999 A brief overview of Forman's discrete Morse theory is presented, from which analogues of the main results of classical Morse theory can be derived for discrete Morse functions, these being functions mapping the set of cells of a CW complex to the real ...
Mathai, Varghese, Yates, Stuart G.
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Discrete Morse Theory for free chain complexes [PDF]
Comptes Rendus. Mathématique, 2005 We extend the combinatorial Morse complex construction to the arbitrary free chain complexes, and give a short, self-contained, and elementary proof of the quasi-isomorphism between the original chain complex and its Morse complex.
Kozlov, Dmitry N.
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Multiparameter Discrete Morse Theory [PDF]
Journal of Applied and Computational Topology, 2022 The main objective of this paper is to extend Morse-Forman theory to vector-valued functions. This is mostly motivated by the need to develop new tools and methods to compute multiparameter persistence. To generalize the theory, in addition to adapting the main definitions and results of Forman to this vectorial setting, we use concepts of ...
Guillaume Brouillette +2 more
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Parameterized Complexity of Discrete Morse Theory [PDF]
ACM Transactions on Mathematical Software, 2016 Optimal Morse matchings reveal essential structures of cell complexes that lead to powerful tools to study discrete geometrical objects, in particular, discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on 3-manifolds through a reduction to the erasability problem.
Benjamin A. Burton +3 more
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Discrete Morse theory and graph braid groups [PDF]
Algebraic & Geometric Topology, 2005 If Gamma is any finite graph, then the unlabelled configuration space of n points on Gamma, denoted UC^n(Gamma), is the space of n-element subsets of Gamma. The braid group of Gamma on n strands is the fundamental group of UC^n(Gamma).
Bridson +8 more
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Smoothing discrete Morse theory [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2016 After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and discrete Morse theory are equivalent, in the sense that every discrete Morse vector on some PL triangulation is also a PL handle vector, and conversely, every PL handle ...
Bruno Benedetti
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Computational discrete Morse theory
, 2012 Basierend auf Formans diskreter Morse Theorie schlage ich in meiner Doktorarbeit einen allgemeinen algorithmischen Ansatz zur Datenanalyse in einer graphentheoretischen Formulierung vor. Dieser rein kombinatorische Ansatz erlaubt es, die extremale Struktur von Skalarfeldern und Vektorfeldern, welche auf diskrete Mannigfaltigkeiten definiert sind, zu ...
Jan Reininghaus
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Discrete Morse theory on digraphs [PDF]
Pure and Applied Mathematics Quarterly, 2021 In this paper, we give a necessary and sufficient condition that discrete Morse functions on a digraph can be extended to be Morse functions on its transitive closure, from this we can extend the Morse theory to digraphs by using quasi-isomorphism between path complex and discrete Morse complex, we also prove a general sufficient condition for digraphs
Lin, Yong, Wang, Chong, Yau, Shing-Tung
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Discrete Morse theory for weighted simplicial complexes [PDF]
Topology and its Applications, 2019 19 pages, to appear in Topology and its ...
Chengyuan Wu +3 more
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Discrete Morse Theory Algorithms
, 2017 Discrete Morse Theory (DMT) is the discrete version of Morse Theory and has been introduced by Robin Forman. Discrete Morse Theory provides a powerful tool for the analysis of topological spaces. The main focus of DMT, like its predecessor Morse theory, is based on finding critical points and constructing a simpler topological space which is homotopy ...
Soroosh Nazem
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