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Showing 1 to 17 of 17 for “"Morse Theory"”.
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Topological Analysis Using Morse Theory and Auditory Display
Finally, we demonstrate the use of wave traversal for creating an auditory display of a simplicial complex. This has application particularly when the complex is large or higher-dimensional, but audio has been shown to reinforce visual display in all cases. The auditory display is intended to …
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Moduli spaces and cw structures arising from morse theory
… the moduli spaces and CW Structures arising from Morse theory.</p> <p>Suppose M is a smooth manifold and f is a Morse function on it. We consider the negative gradient flow of f. Suppose the flow satisfies transversality. This naturally defines the moduli spaces of flow lines and gives a …
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Stationary Configurations of Point Vortices (Morse Theory, Hamiltonian Systems, Fluid Mechanics)
The motion of point vortices in a plane of fluid is an old problem of fluid mechanics, which was given a Hamiltonian formulation by Kirchhoff. Stationary configurations are those which remain self-similar throughout the motion, and are of considerable physical interest.
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Turing Decidability and Computational Complexity of MorseHomology
… thesis presents a general background on discrete Morse theory, as developed by Robin Forman, as well as an introduction to computability and computational complexity. Since general point-set data equipped with a smooth structure can admit a triangulation, discrete Morse theory finds numerous …
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Dynamic Modeling With Implicit Surfaces and Polygonal Meshes
"Morse theory reveals the topological structure of a shape based on the critical points of a real function over the shape. This thesis solves a relaxed form of Laplace's equation to find a ""fair"" Morse function with a user-controlled number and configuration of critical points."
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A semi-infinite cycle construction of Floer homology
… with the foundations of a new approach to Floer theory. As opposed to the traditional approach, which can be viewed as a generalization of Morse theory to an infinite dimensional setting, our approach is a generalization of bordism to infinite dimensions. The key new insight, based on unpublished …
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Functions with minimal number of critical points
… Takens in 1968. Inspired by Takens' paper and by Morse theory in the Smale setting we have analyzed the crit for products of manifolds. Using concepts from the graph theory we have found upper bounds of crit for products of special manifolds with generalized tori. The proofs of these results are …
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Configuration spaces of thick particles on graphs
… graph. Our main tool is a piecewise linear (PL) Morse-Bott theory for affine polytope complexes, which extends the Morse theory for such complexes introduced by M. Bestvina and N. Brady. As the size parameter r increases, the topological properties of the corresponding configuration spaces vary. …
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Circle-Valued Generating Family Invariants
<p>Legendrian knot theory is the study of topological knots and links that satisfy an additional, geometric condition. This condition, imposed by a contact structure, makes it possible for certain knots to be topologically equivalent without being Legendrian equivalent. In recent years, real-valued …
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Topological analysis of singularity loci for serial and parallel manipulators
… work proposes a numerical procedure based upon Morse theory, an important branch of differential topology. Such procedure counts and identify the singularity-free regions that are cut by the singularity locus out of the configuration space, and the disjoint regions composing the configuration …
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Topology of Closed 1-Forms on Manifolds with Boundary
… on it. This is the essential motivation of Morse theory and many of its generalisations from a modern viewpoint. One fruitful direction of the generalisation of the theory is to look at the zeros of a closed 1-form which can be viewed locally as a real function up to an additive constant, …
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Topological Approaches to Chromatic Number and Box Complex Analysis of Partition Graphs
… techniques. Lastly, we apply discrete Morse theory to construct a simplicial complex homotopy equivalent to the box complex of P(33), using two methods: elementary collapses and the determination of a discrete Morse function on the box complex. This process reduces the dimension of the …
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Topics on critical point theory
… only assumed to be C1and therefore the classical Morse theory is not available. In order to do this, we isolate various topological indices that can be associated with certain critical sets and points. If the functionals are C2 and the critical points are non-degenerated, these indices can then be …
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Isosurface Interactions Within Turbulent Premixed Hydrogen and Hydrocarbon Flames
… interactions can be identified with the help of Morse theory of critical points and the local topology at critical points can be evaluated. In previous studies, the interactions have been categorised into four different groups, namely reactant pocket, tunnel formation, tunnel closure and product …
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Stochastic Microlensing: Mathematical Theory and Applications
… we initiate the development of a mathematical theory </p><p>of stochastic microlensing. We first construct a natural probability space for stochastic microlensing and characterize the general behaviour of the random time </p><p>delay functions' random critical sets. Next we study stochastic …
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Topology of configuration space on trees
Configuration Space on trees comes naturally from problems in engineering and has its own importance in mathematics. This paper reviewed the existing research results on the topological properties of classic configuration spaces and generalized some of them for the no-k-equal configuration space on …
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Lefschetz fixed point theory and morse inequalities on stratified pseudomanifolds
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2025-02-04 without embargo terms