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Three-manifolds. Classical results

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Literature Cited

  1. Yu. G. Borisovich, N. M. Blisniakov, N. M. Israelevich, and T. N. Fomenko,Introduction to Topology. Textbook for Students with a Speciality in Mathematics [in Russian] Vysshaya Shkola, Moscow (1980).

    Google Scholar 

  2. O. Ya. Viro, “Linkings, two-sheeted branched coverings, and braids,”Mat.Sb.,87, No. 2, 216–228. (1972).

    MATH  MathSciNet  Google Scholar 

  3. V. L. Kobelsky, “The Volodin-Kuznetsov-Fomenko hypothesis on Heegaard diagrams of a 3-sphere is not correct,”Uspekhi Mat. Nauk,32, No. 5, 175–176 (1977).

    Google Scholar 

  4. I. A. Volodin, V. E. Kuznetsov, and A. T. Fomenko, “The problem of discriminating algorithmically the standard three-dimensional shhere,”Uspekhi Mat. Nauk,29, No. 5, 71–168 (1974).

    Google Scholar 

  5. G. Seifert and F. Trelfall,Topology [in Russian], GONTI, Moscow-Leningrad (1938).

    Google Scholar 

  6. W. Massi and J. Strollings,Algebraic Topology. An Introduction [Russian translation], Mir, Moscow (1977).

    Google Scholar 

  7. S. V. Matveev, “Transformations of special spines and the Zeeman hypothesis,”Izv. Akad. Nauk SSSR, Ser. Mat.,51, No. 5, 1104–1116 (1987).

    MATH  Google Scholar 

  8. S. V. Matveev, “Complexity additiveness and the Haken method in the topology of 3-manifolds,”Ukr. Mat. Zh.,41, No. 9, 1234–1240 (1989).

    MATH  Google Scholar 

  9. S. V. Matveev and A. T. Fomenko, “Isoenergetic surfaces of Hamiltonian systems, the numeration of 3-manifolds in the order of their complexity's increase, and computation of volumes of closed hyperbolic manifolds,”Uspekhi Mat. Nauk,43, No. 1, 5–22 (1988).

    MathSciNet  Google Scholar 

  10. C. P. Novikov, “Topology,” In: Sovremennye Problemy Matematiki. Fundamentalnye dostizheniya, 12.Itogi Nauki i Tekh., All-Union Inst. for Scientific and Technical Information (VINITI), Akademia Nauk SSSR, Moscow (1986), pp. 5–252.

    Google Scholar 

  11. V. A. Rokhlin and D. B. Fuks,The Beginning of Topology. Geometrical Chapters [In Russian], Nauka, Moscow (1977).

    Google Scholar 

  12. P. Scott,The Geometries over 3-Manifolds [Russian Translation], Mir, Moscow (1986).

    Google Scholar 

  13. V. G. Turaev,On the Topological Classification of Geometrical 3-Manifolds, [in Russian], Preprint LOMI, No. P-7, Leningrad (1986).

  14. A. T. Fomenko, “The topology of equal energy surfaces of integrable Hamiltonian systems and the obstacles to their integrability,”Izv. Akad. Nauk SSSR, Ser. Mat.,50, No. 6, 1276–1307 (1986).

    MATH  MathSciNet  Google Scholar 

  15. J. W. Alexander, “Note on Riemann spaces,”Bull. Amer. Math. Soc.,26, 370–372 (1920).

    Google Scholar 

  16. J. S. Birman and H. M. Hilden, “Heegaard splittings of branched coverings of S3,”Trans. Amer. Math. Soc.,213, 315–352 (1975).

    MathSciNet  Google Scholar 

  17. B. G. Casler, “An embedding theorem for connected 3-manifolds with boundary,”Proc. Amer. Math. Soc.,16, No. 4, 559–566 (1965).

    MATH  MathSciNet  Google Scholar 

  18. W. Haken, “Theorie der Normalflächen. Ein Isotopierkriterium für den Kreisknoten,”Acta Math.,105, No. 3, 245–375 (1961).

    MATH  MathSciNet  Google Scholar 

  19. G. Hemion, “On the classification of homeomorphisms of 2-manifolds and the classification of 3-manifolds,”Acta Math.,142, No. 1, 123–155 (1979).

    MATH  MathSciNet  Google Scholar 

  20. J. Hempel, “3-manifolds,”Ann. Math. Stud., No. 86, 195 (1976).

    MATH  MathSciNet  Google Scholar 

  21. H. M. Hilden, M. T. Lozano, and J. M. Montesinos, “Universal knots,”Lect. Notes Math.,1144, 25–59 (1985).

    Google Scholar 

  22. T. Homma, M. Ochiai, and M. Takahashi, “An algorithm for recognizingS 3 in manifolds with Heegaard splittings of genus two,”Osaka J. Math.,17, 625–648 (1980).

    MathSciNet  Google Scholar 

  23. K. Johannson, “Homotopy equivalences of 3-manifolds with boundaries,”Lect. Notes Math.,761, 1–303 (1979).

    MathSciNet  Google Scholar 

  24. S. Kaplan, “Constructing framed 4-manifolds with given almost framed boundaries,”Trans. Amer. Math. Soc.,254, 237–263 (1979).

    MATH  MathSciNet  Google Scholar 

  25. W. B. R. Lickorish, “A representation of orientable combinatorial 3-manifolds,”Ann. Math.,76, No. 3, 531–540 (1962).

    MATH  MathSciNet  Google Scholar 

  26. S. V. Matveev, “Complexity theory of three dimensional manifolds,”Acta Appl. Math.,19, 101–130. (1990).

    MATH  MathSciNet  Google Scholar 

  27. J. W. Milnor, “A unique factorisation decomposition theorem for 3-manifolds,”Amer. J. Math.,84, No. 1, 1–7 (1962).

    MATH  MathSciNet  Google Scholar 

  28. E. E. Moise, “Affine structures in 3-manifolds. V. The triangulation theorem and Hauptvermuttung,”Ann. Math.,56, 96–144 (1952).

    MATH  MathSciNet  Google Scholar 

  29. J. M. Montesinos, “Three-manifolds as 3-fold branched covers ofS 3,”Quart. J. Math.,27, No. 105, 85–94 (1976).

    MATH  MathSciNet  Google Scholar 

  30. I. W. Morgan and H. Bass,The Smyth Conjecture, Academic Press, New York (1984).

    Google Scholar 

  31. K. Reidemeister, “Zur dreidimensionalen Topologie,”Abh. Math. Sem. Univ., Hamburg, No. 9, 189–194 (1933).

    MATH  Google Scholar 

  32. Z. Sela,The Homeomorphism Problem for Geometric 3-Manifolds and Equations in Hyperbolic Groups. Preprint, Hebrew Univ., Jerusalem (1990).

    Google Scholar 

  33. P. B. Shalen, “A ‘piecewise-linear’ method for triangulating 3-manifolds,”Adv. Math.,52, No. 1, 34–80 (1984).

    MATH  MathSciNet  Google Scholar 

  34. P. Smyth, “Transformations of finite period,”Ann. Math.,39, 127–164 (1938).

    Google Scholar 

  35. W. Thurston, “The geometry and topology of 3-manifolds,”Lect. Notes Math. (1977).

  36. F. Waldhausen, “Heegaard-Zerlegungen der 3-Sphäre,”Topology,7, No. 2, 195–203 (1968).

    MATH  MathSciNet  Google Scholar 

  37. F. Waldhausen, “Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I, II,”Invent Math.,3, No. 4, 308–333 (1967); 4; No. 2, 87–117 (1967).

    MATH  MathSciNet  Google Scholar 

  38. F. Waldhausen, “Über Involution der 3-Sphäre,”Topology,8, No. 1, 81–91 (1969).

    MATH  MathSciNet  Google Scholar 

  39. F. Waldhausen, “On irreducible 3-manifolds which are sufficiently large,”Ann. Math.,87, No. 1, 56–88 (1968).

    MATH  MathSciNet  Google Scholar 

  40. J. Weeks,Hyperbolic Structures on Three-Manifolds, Princeton Ph. D. thesis (1985).

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  1. S. V. Matveev
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 6, Topologiya-1, 1993.

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Matveev, S.V. Three-manifolds. Classical results. J Math Sci 74, 834–860 (1995). https://doi.org/10.1007/BF02362845

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