The number of split points of a Morse form and the structure of its foliation

[1] ARNOUX, P.— LEVITT, G.: Sur l’unique ergodicité des 1-formes fermées singulières, Invent. Math. 84 (1986), 141–156. http://dx.doi.org/10.1007/BF0138873610.1007/BF01388736Search in Google Scholar

[2] CAMACHO, C.— SCARDUA, B.: On codimension one foliations with Morse singularities on three-manifolds, Topology Appl. 154 (2007), 1032–1040. http://dx.doi.org/10.1016/j.topol.2006.10.00510.1016/j.topol.2006.10.005Search in Google Scholar

[3] CAMACHO, C.— SCARDUA, B.: On foliations with Morse singularities, Proc. Amer. Math. Soc. 136 (2008), 4065–4073. http://dx.doi.org/10.1090/S0002-9939-08-09371-410.1090/S0002-9939-08-09371-4Search in Google Scholar

[4] FARBER, M.: Topology of Closed One-forms. Math. Surveys Monogr. 108, Amer. Math. Soc., Providence, RI, 2004. 10.1090/surv/108Search in Google Scholar

[5] GELBUKH I.: Presence of minimal components in a Morse form foliation, Differential Geom. Appl. 22 (2005), 189–198. http://dx.doi.org/10.1016/j.difgeo.2004.10.00610.1016/j.difgeo.2004.10.006Search in Google Scholar

[6] GELBUKH I.: Number of minimal components and homologically independent compact leaves for a Morse form foliation, Studia Sci. Math. Hungar. 46 (2009), 547–557. Search in Google Scholar

[7] GELBUKH I.: On the structure of a Morse form foliation, Czechoslovak Math. J. 59 (2009), 207–220. http://dx.doi.org/10.1007/s10587-009-0015-510.1007/s10587-009-0015-5Search in Google Scholar

[8] GELBUKH I.: Foliations of close cohomologous Morse forms, Czechoslovak Math. J. (2013) (To appear). 10.1007/s10587-013-0034-0Search in Google Scholar

[9] GELBUKH I.: The number of minimal components and homologically independent compact leaves of a weakly generic Morse form on a closed surface, Rocky Mountain J. Math. (2013) (To appear). 10.1216/RMJ-2013-43-5-1537Search in Google Scholar

[10] GELBUKH I.: Ranks of collinear Morse forms, J. Geom. Phys. 61 (2011), 425–435. http://dx.doi.org/10.1016/j.geomphys.2010.10.01010.1016/j.geomphys.2010.10.010Search in Google Scholar

[11] GUILLEMIN, V.— POLLACK, A.: Differential Topology, Prentice-Hall, New York, NY, 1974. Search in Google Scholar

[12] HARARY, F.: Graph Theory, Addison-Wesley Publ. Comp., Massachusetts, 1994. Search in Google Scholar

[13] HIRSCH, M. W.: Smooth regular neighborhoods, Ann. of Math. (2) 76 (1962), 524–530. http://dx.doi.org/10.2307/197037210.2307/1970372Search in Google Scholar

[14] KATOK, A.: Invariant measures for flows on oriented surfaces, Soviet. Math. Dokl. 14 (1973), 1104–1108. Search in Google Scholar

[15] LEVITT, G.: 1-formes fermées singulières et groupe fondamental, Invent. Math. 88 (1987), 635–667. http://dx.doi.org/10.1007/BF0139183510.1007/BF01391835Search in Google Scholar

[16] LEVITT, G.: Groupe fondamental de l’espace des feuilles dans les feuilletages sans holonomie, J. Differential Geom. 31 (1990), 711–761. 10.4310/jdg/1214444632Search in Google Scholar

[17] MEL’NIKOVA, I.: A test for non-compactness of the foliation of a Morse form, Russian Math. Surveys 50 (1995), No. 2, 444–445. http://dx.doi.org/10.1070/RM1995v050n02ABEH00209210.1070/RM1995v050n02ABEH002092Search in Google Scholar

[18] MEL’NIKOVA, I.: Noncompact leaves of foliations of Morse forms, Math. Notes 63 (1998), 760–763. http://dx.doi.org/10.1007/BF0231276910.1007/BF02312769Search in Google Scholar

[19] MILNOR, J.: Morse Theory. Ann. of Math. Stud. 51, Princeton University Press, Princeton, NJ, 1963. 10.1515/9781400881802Search in Google Scholar

[20] MILNOR, J.: Lectures on the h-Cobordism Theorem. Math. Notes, No. 1, Princeton University Press, Princeton, NJ, 1965. 10.1515/9781400878055Search in Google Scholar

[21] NOVIKOV, S.: The Hamiltonian formalism and a multi-valued analogue of Morse theory, Russian Math. Surveys 37 (1982), No. 5, 1–56. http://dx.doi.org/10.1070/RM1982v037n05ABEH00402010.1070/RM1982v037n05ABEH004020Search in Google Scholar

[22] PEDERSEN, E. K.: Regular neighborhoods in topological manifolds, Michigan Math. J. 24 (1977), 177–183. http://dx.doi.org/10.1307/mmj/102900188110.1307/mmj/1029001881Search in Google Scholar