منابع مشابه
The modular class of a regular Poisson manifold and the Reeb invariant of its symplectic foliation
1 We show that, for any regular Poisson manifold, there is an injective natural linear map from the first leafwise cohomology space into the first Poisson cohomology space which maps the Reeb class of the symplectic foliation to the modular class of the Poisson manifold. The Riemannian interpretation of those classes will permit us to show that a regular Poisson manifold whose symplectic foliat...
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The Reeb graph is a construction which originated in Morse theory to study a real valued function defined on a topological space. More recently, it has been used in various applications to study noisy data which creates a desire to define a measure of similarity between these structures. Here, we exploit the fact that the category of Reeb graphs is equivalent to the category of a particular cla...
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Tracking features and exploring their temporal dynamics can aid scientists in identifying interesting time intervals in a simulation and serve as basis for performing quantitative analyses of temporal phenomena. In this paper, we develop a novel approach for tracking subsets of isosurfaces, such as burning regions in simulated flames, which are defined as areas of high fuel consumption on a tem...
متن کاملBook embeddings of Reeb graphs
Let X be a simplicial complex with a piecewise linear function f : X → R. The Reeb graph Reeb(f,X) is the quotient of X, where we collapse each connected component of f−1(t) to a single point. Let the nodes of Reeb(f,X) be all homologically critical points where any homology of the corresponding component of the level set f−1(t) changes. Then we can label every arc of Reeb(f,X) with the Betti n...
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ژورنال
عنوان ژورنال: Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics
سال: 1997
ISSN: 1303-5991
DOI: 10.1501/commua1_0000000420