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Equivalence of closed 1-forms on surfaces with edge

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We investigate closed 1-forms with isolated zeros on surfaces with edge. A criterion for the topological equivalence of closed 1-forms is proved.

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References

  1. A. A. Oshemkov, “Morse functions on two-dimensional surfaces. Coding of singularities,” Tr. Inst. Mat. Ros. Akad. Nauk, 205, 131–140 (1994).

    Google Scholar 

  2. V. V. Sharko, “On topological equivalence Morse functions on surfaces,” in: International Conference “Low-Dimensional Topology and Combinatorial Group Theory,” Chelyabinsk State University, Chelyabinsk (1996), pp. 19–23.

  3. S. I. Maksimenko, “Classification of m-functions on surfaces,” Ukr. Mat. Zh., 51, No. 8, 1129–1135 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  4. A. O. Prishlyak, ”Topological classification of m-fields on two- and three-dimensional manifolds,” Ukr. Mat. Zh., 55, No. 6, 799–805 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  5. S. Kh. Aranson and V. Z. Grines, “Topological classification of flows on closed surfaces,” Usp. Mat. Nauk, 41, Issue 1(247), 149–169 (1986).

    MathSciNet  Google Scholar 

  6. S. Kh. Aranson and V. Z. Grines, “On some invariants of dynamical systems on two-dimensional manifolds (necessary and sufficient conditions for the topological equivalence of transitive systems),” Mat. Sb., 90(132), No. 3, 372–401 (1973).

    MathSciNet  Google Scholar 

  7. S. Kh. Aranson, E. V. Zhuzhoma, and I. A. Tel’nykh, “Transitive and supertransitive flows on closed nonoriented surfaces,” Mat. Zametki, 63, Issue 4, 625–628 (1998).

    MathSciNet  Google Scholar 

  8. S. V. Bilun and O. O. Pryshlyak, “Closed Morse 1-forms on closed surfaces,” Visn. Kyiv. Univ., Ser. Mat. Mekh., No. 8, 77–81 (2002).

  9. S. V. Bilun and O. O. Pryshlyak, “Closed Morse 1-forms with isolated critical points on closed oriented surfaces,” Visn. Kyiv. Univ., Ser. Mat. Mekh., No. 18, 66–69 (2007).

  10. N. V. Budnyts’ka and O. O. Pryshlyak, “Equivalence of closed 1-forms on oriented surfaces,” Visn. Kyiv. Univ., Ser. Mat. Mekh., No. 19, 36–38 (2008).

  11. N. V. Budnyts’ka, “Equivalence of closed 1-forms on closed nonoriented surfaces,” Nelin. Kolyvannya, 12, No. 2, 155–167 (2009).

    Google Scholar 

  12. A. O. Prishlyak, “Topological equivalence of smooth functions with isolated critical points on a closed surface,” Topol. Appl., No. 119, pp. 257–267 (2002).

    Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 11, pp. 1455–1472, November, 2009.

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Budnyts’ka, N.V., Pryshlyak, O.O. Equivalence of closed 1-forms on surfaces with edge. Ukr Math J 61, 1710–1727 (2009). https://doi.org/10.1007/s11253-010-0308-8

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  • DOI: https://doi.org/10.1007/s11253-010-0308-8

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