Results 1 to 10 of about 57,225 (134)
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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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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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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The Elser nuclei sum revisited [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 Fix a finite undirected graph $\Gamma$ and a vertex $v$ of $\Gamma$. Let $E$ be the set of edges of $\Gamma$. We call a subset $F$ of $E$ pandemic if each edge of $\Gamma$ has at least one endpoint that can be connected to $v$ by an $F$-path (i.e., a ...
Darij Grinberg
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Nontrivial solutions of discrete Kirchhoff-type problems via Morse theory
Advances in Nonlinear Analysis, 2022 In this article, we study discrete Kirchhoff-type problems when the nonlinearity is resonant at both zero and infinity. We establish a series of results on the existence of nontrivial solutions by combining variational method with Morse theory.
Long Yuhua
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Multiple Periodic Solutions to Nonlinear Discrete Hamiltonian Systems
Advances in Difference Equations, 2007 An existence result of multiple periodic solutions to the asymptotically linear discrete Hamiltonian systems is obtained by using the Morse index theory.
Bo Zheng
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Merging Discrete Morse Vector Fields: A Case of Stubborn Geometric Parallelization
Algorithms, 2021 We address the basic question in discrete Morse theory of combining discrete gradient fields that are partially defined on subsets of the given complex. This is a well-posed question when the discrete gradient field V is generated using a fixed algorithm
Douglas Lenseth, Boris Goldfarb
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Parameterized Complexity of Discrete Morse Theory [PDF]
ACM Transactions on Mathematical Software, 2013 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.
Burton, Benjamin A. +3 more
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Combinatorial Topology of Toric arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 We prove that the complement of a complexified toric arrangement has the homotopy type of a minimal CW-complex, and thus its homology is torsion-free.
Giacomo d'Antonio, Emanuele Delucchi
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