Zobrazeno 1 - 10 of 25 pro vyhledávání: '"Irina Gelbukh"'
1
Reeb graphs of circle-valued functions: A survey and basic facts
Autor: Irina Gelbukh
Publikováno v: Topological Methods in Nonlinear Analysis. :1-23
The Reeb graph of a circle-valued function is a topological space obtained by contracting connected components of level sets (preimages of points) to points. For some smooth functions, the Reeb graph has the structure of a finite graph. This notion f
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::2c5bcf7581ea4e9cb80fbdd6c363d1bb
https://doi.org/10.12775/tmna.2022.023
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2
Realization of a graph as the Reeb graph of a height function on an embedded surface
Autor: Irina Gelbukh
Publikováno v: Topological Methods in Nonlinear Analysis. :1-20
We show that for a given finite graph $G$ without loop edges and isolated vertices, there exists an embedding of a closed orientable surface in $\mathbb{R}^3$ such that the Reeb graph of the associated height function has the structure of $G$. In par
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a88e4f6e09380616961bf1ccb0c54eeb
https://doi.org/10.12775/tmna.2021.058
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4
Realization of a Graph as the Reeb Graph of a Morse–Bott or a Round Function
Autor: Irina Gelbukh
Publikováno v: Studia Scientiarum Mathematicarum Hungarica. 59:1-16
We prove criteria for a graph to be the Reeb graph of a function of a given class on a closed manifold: Morse–Bott, round, and in general smooth functions whose critical set consists of a finite number of submanifolds. The criteria are given in ter
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::232a65dc3fade7f563f2dabaf4daa421
https://doi.org/10.1556/012.2022.01512
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7
A finite graph is homeomorphic to the Reeb graph of a Morse–Bott function
Autor: Irina Gelbukh
Publikováno v: Mathematica Slovaca. 71:757-772
We prove that a finite graph (allowing loops and multiple edges) is homeomorphic (isomorphic up to vertices of degree two) to the Reeb graph of a Morse–Bott function on a smooth closed n-manifold, for any dimension n ≥ 2. The manifold can be chos
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::780577118571e2627f3c7668a058cf51
https://doi.org/10.1515/ms-2021-0018
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8
Morse-Bott functions with two critical values on a surface
Autor: Irina Gelbukh
Publikováno v: Czechoslovak Mathematical Journal. 71:865-880
We study Morse-Bott functions with two critical values (equivalently, non-constant without saddles) on closed surfaces. We show that only four surfaces admit such functions (though in higher dimensions, we construct many such manifolds, e.g. as fiber
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::e004075888ed90fca0e54597656cf5ff
https://doi.org/10.21136/cmj.2021.0125-20
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10
Approximation of metric spaces by Reeb graphs: Cycle rank of a Reeb graph, the co-rank of the fundamental group, and large components of level sets on Riemannian manifolds
Autor: Irina Gelbukh
Publikováno v: Filomat. 33:2031-2049
For a connected locally path-connected topological space $X$ and a continuous function $f$ on it such that its Reeb graph $R_f$ is a finite topological graph, we show that the cycle rank of $R_f$, i.e., the first Betti number $b_1(R_f)$, in computati
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11e8884ba333efcbb17a48ab6e8a8784
https://doi.org/10.2298/fil1907031g
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