Irina Gelbukh

Ph.D. (mathematics)

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 Microsoft Academic



. Topological Methods in Nonlinear Analysis, submitted, 2021.
  1. Irina Gelbukh. A finite graph is homeomorphic to the Reeb graph of a Morse–Bott function. Mathematica Slovaca, 71(3):757–772, 2021; doi: 10.1515/ms-2021-0018.

  2. item 25

    Irina Gelbukh. an immersion in 3.

  3. Key words: Reeb graph, Morse–Bott function, immersion, height function, surface

  4. item 25

    Irina Gelbukh. Morse–Bott functions with two critical values on a surface. Czechoslovak Mathematical Journal, 71(3):865–880, 2021; doi: 10.21136/CMJ.2021.0125-20.

  • Key words: Reeb graph; height function; Morse–Bott function; orientable surface; embedding.

  • MSC 2020: Primary: 57R40, 53A05; secondary: 58K05, 57R45.

  • Irina Gelbukh. Morse–Bott functions with two critical values on a surface. Czechoslovak Mathematical Journal, 71(3):865–880, 2021; doi: 10.21136/CMJ.2021.0125-20.

  • Irina Gelbukh. 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. Filomat, 33(7):2031–2049, 2019; doi: 10.2298/FIL1907031G.

  • Irina Gelbukh. Compact and locally dense leaves of a closed one-form foliation. Journal of Mathematical Analysis and Applications, 464:1275–1289, 2018; doi: 10.1016/j.jmaa.2018.04.053.

  • Irina Gelbukh. Loops in Reeb graphs of n-manifolds. Discrete & Computational Geometry, 59(4):843–863, 2018; doi: 10.1007/s00454-017-9957-9.

  • Irina Gelbukh. Sufficient conditions for the compactifiability of a closed one-form foliation. Turkish Journal of Mathematics, 41:1344–1353, 2017; doi: 10.3906/mat-1602-95.

  • Irina Gelbukh. Isotropy index for the connected sum and the direct product of manifolds. Publicationes Mathematicae Debrecen, 90(3–4):287–310, 2017; doi: 10.5486/PMD.2017.7409.

  • Irina Gelbukh. The co-rank of the fundamental group: the direct product, the first Betti number, and the topology of foliations. Mathematica Slovaca, 67(3):645–656, 2017; Zbl 06738450; doi: 10.1515/ms-2016-0298.

  • Irina Gelbukh. Co-rank and Betti number of a group. Czechoslovak Mathematical Journal, 65(2):565567, ; Zbl 1363.20034; doi: 10.1007/s10587-015-0195-0.

  • Irina Gelbukh. The number of minimal components and homologically independent compact leaves of a weakly generic Morse form on a closed surface. Rocky Mountain Journal of Mathematics, 43(5):1537–1552, 2013; Zbl 1280.57021; doi: 10.1216/RMJ-2013-43-5-1537.

  • Irina Gelbukh. Close cohomologous Morse forms with compact leaves. Czechoslovak Mathematical Journal, 63(2):515–528, 2013; Zbl 1289.57009; doi: 10.1007/s10587-013-0034-0.

  • Irina Gelbukh. The number of split points of a Morse form and the structure of its foliation. Mathematica Slovaca, 63(2):331–348, 2013; Zbl 1324.57004; doi: 10.2478/s12175-013-0101-x.

  • Irina Gelbukh. Structure of a Morse form foliation on a closed surface in terms of genus. Differential Geometry and its Applications, 29(4):473–492, 2011; Zbl 1223.57022; doi: 10.1016/j.difgeo.2011.04.029.

  • Irina Gelbukh. On collinear closed one-forms. Bulletin of the Australian Mathematical Society, 84(2):322–336, 2011; Zbl 1226.57040; doi: 10.1017/S0004972711002310.

  • Irina Gelbukh. On compact leaves of a Morse form foliation. Publicationes Mathematicae Debrecen, 78(1):37–48, 2011; Zbl 1240.57011; doi: 10.5486/PMD.2011.4369.

  • Irina Gelbukh. Ranks of collinear Morse forms. Journal of Geometry and Physics, 61(2):425–435, 2011; Zbl 1210.57027; doi: 10.1016/j.geomphys.2010.10.010.

  • Irina Gelbukh. Number of minimal components and homologically independent compact leaves for a Morse form foliation. Studia Scientiarum Mathematicarum Hungarica, 46(4):547–557, 2009; Zbl 1274.57005; doi: 10.1556/SScMath.2009.1108.

  • Irina Gelbukh. On the structure of a Morse form foliation. Czechoslovak Mathematical Journal, 59(1):207–220, 2009; Zbl 1224.57010; doi: 10.1007/s10587-009-0015-5.

  • Irina Gelbukh. Presence of minimal components in a Morse form foliation. Differential Geometry and its Applications, 22(2):189–198, 2005; Zbl 1070.57016; doi: 10.1016/j.difgeo.2004.10.006.

  • I.A. Mel'nikova. Maximal isotropic subspaces of skew-symmetric bilinear mapping. Moscow University Mathematics Bulletin 54(4):1–3, 1999; Zbl 0957.57018.
    Translated from: И.А. Мельникова. Максимальные изотропные подпространства кососимметрического билинейного отображения. Вестник МГУ, Сер. матем., мех. 4:3–5, 1999.

  • I.A. Mel'nikova. Noncompact leaves of foliations of Morse forms. Mathematical Notes 63(6):760–763, June 1998; Zbl 0917.57022; doi: 10.1007/BF02312769.
    Translated from: И.А. Мельникова. Некомпактные слои слоения морсовской формы. Математические заметки 63(6):862–865, 1998.

  • I.A. Mel'nikova. Properties of Morse forms that determine compact foliations on Mg2. Mathematical Notes 60(6):714–716, 1996; Zbl 0898.57012; doi: 10.1007/BF02305168.
    Translated from: И.А. Мельникова. Свойства морсовской формы, определяющей компактное слоение на Mg2. Математические заметки 60(6):942–945, 1996.

  • I.A. Mel'nikova. Singular points of a Morsian form and foliations. Moscow University Mathematics Bulletin 51(4):33–36, 1996; Zbl 0914.58006.
    Translated from: И.А. Мельникова. Особые точки морсовской формы и слоения. Вестник МГУ, Сер. матем., мех. 4:37–40, 1996.

  • I.A. Mel'nikova. A test for compactness of a foliation. Mathematical Notes 58(6):1302–1305, 1995; Zbl 0857.57030; doi: 10.1007/BF02304889.
    Translated from: И.А. Мельникова. Признак компактности слоения. Математические заметки 58(6):872–877, 1995.

  • I.A. Mel'nikova. A test for non-compactness of the foliation of a Morse form. Russian Mathematical Surveys 50(2):444–445, 1995; Zbl 0859.58005; doi: 10.1070/RM1995v050n02ABEH002092.
    Translated from: И.А. Мельникова. Признак некомпактности слоения морсовской формы. Успехи математических наук 50(3):217–218, 1995.

  • I.A. Mel'nikova. An indicator of the noncompactness of a foliation on Mg2. Mathematical Notes 53(3):356–358, 1993; Zbl 0809.57018; doi: 10.1007/BF01207728.
    Translated from: И.А. Мельникова. Признак некомпактности слоения на Mg2. Математические заметки 53(3):158–160, 1993.

  • Conference papers and talks

    1. Irina Gelbukh. Realization of a graph as the Reeb graph of a Morse, Morse–Bott or round function. International Online Conference "Algebraic and Geometric Methods of Analysis" dedicated to the memory of Yuriy Trokhymchuk (17.03.1928–18.12.2019), Odessa, Ukraine, May 25–28, 2021.

    2. Irina Gelbukh. Topology of the Reeb graph. Howard Mathematics Colloquium, Howard University, Washington DC, March 26, 2021.

    3. Irina Gelbukh. Keynote talk. 3rd International Conference on Innovations in Computing, CGC College of Engineering, Mohali, Punjab, India, 12–13 December 2019.

    4. Irina Gelbukh. Rank of a maximal subgroup in H1(M,) with trivial cup-product. Fourth International Conference of Applied Mathematics and Computing (FICAMC), Plovdiv, Bulgaria, August 12–18, 2007.

    5. I.A. Melnikova. Compact foliations of a Morse form on Mg2. International Conference on Topology and Applications in memory of P.S. Alexandroff (1896–1982). Moscow, Russia, May 27–31, 1996.

    PhD thesis

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    Last modified 2021-03-28
    Abstracts in separate files, for Google Scholar's pleasure.