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Über das geschlecht und die faserbarkeit von montesinos-knoten

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Literatur

  1. E. Artin, Theorie der Zöpfe, Abh. Math. Sem. Univ. Hamburg4, 47–72 (1926).

    Google Scholar 

  2. C. Bankwitz, G. Schumann, Über Viergeflechte. Abh. Math. Sem. Univ. Hamburg10, 263–284 (1934).

    Article  Google Scholar 

  3. J. S. Birman, Braid, links, and mapping class groups. Ann. Math. Studies, Princeton Univ. Press, Princeton Nr. 7 (1974).

    Google Scholar 

  4. M. Boileau,L. Siebenmann, A planar classification of Pretzel knots and Montesinos knots. Prepublications of the Univ. Paris-Sud 80 T 38 (1980).

  5. G. Burde, Zur Theorie der Zöpfe. Math. Ann.151, 101–107 (1963).

    Article  MATH  MathSciNet  Google Scholar 

  6. G. Burde, Verschlingungsinvariante von Knoten und Verkettungen mit zwei Brücken. Math. Z.145, 235–242 (1975).

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Conway, An enumeration of knots and links and some of their related properties. Computational problems in Abstract Algebra, 329–358, New York, Pergamon Press (1970).

    Google Scholar 

  8. R. H. Crowell, Genus of alternating link types. Ann. Math.69, 258–275 (1959).

    Article  MathSciNet  Google Scholar 

  9. K. Funcke, Geschlecht von Knoten mit zwei Brucken und die Faserbarkeit ihrer Außenräume. Math. Z.159, 2–24 (1978).

    Article  MathSciNet  Google Scholar 

  10. D. Gabai, The Murasugi sum is a natural geometric operation. Contemporary Mathematics, AMS,20, 131–143 (1983).

    MATH  MathSciNet  Google Scholar 

  11. R. I. Hartley, On two-bridged knots polynomials. J. Austral. Math. Soc.28, 241–249 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  12. F. Hosokawa, On Δ-polynomials of links. Osaka Math. J.10, 273–282 (1953).

    MathSciNet  Google Scholar 

  13. T. Kanenobu, The augmentation subgroup of a pretzel link. Math. Sem. Notes Kobe Univ.7, 363–385 (1979).

    MathSciNet  Google Scholar 

  14. L. H. Kauffman, The Conway polynomial. Topology20, 101–108 (1980).

    Article  MathSciNet  Google Scholar 

  15. B. W. Jones, The arithmetic Theory of Quadratic forms. The Carus Math. Monogr. N.10 (1950).

  16. J. M. Montesinos, Variedades de Seifert que son recubridores ciclicos ramificados de hos johas. Bol. Soc. Mat. Mexicana18, 1–32 (1973).

    MATH  MathSciNet  Google Scholar 

  17. J. M. Montbsinos, Revêtements ramifiés de noeuds, espace fibrés de Seifert et scindements de Heegaard. Prepublications Orsay (1979).

  18. K. Murasugi, On alternating knots. Osaka Math. J.12, 277–303 (1960).

    MATH  MathSciNet  Google Scholar 

  19. K. Murasugi, On a certain subgroup of the group of an alternating link. Amer. J. Math.85, 544–550 (1963).

    Article  MATH  MathSciNet  Google Scholar 

  20. K. Murasugi, On a certain numerical invariant of link types. Trans. Amer. Math. Soc.117, 387–422 (1965).

    Article  MATH  MathSciNet  Google Scholar 

  21. K. Murasugi, On the signature of links. Topology9, 283–298 (1970).

    Article  MathSciNet  Google Scholar 

  22. L. Neuwirth, The algebraic determination of the genus of a knot. Amer. J. Math.82, 791–798 (1960).

    Article  MATH  MathSciNet  Google Scholar 

  23. K. A. Perko, On dihedral covering spaces of knots. Invent, math.34, 77–84 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  24. O. Perron, Die Lehre von den Kettenbruchen, Bd. I und II. B. G. Teubner, Stuttgart (1954).

    Google Scholar 

  25. T. C. V. Quách, Invariants des noeuds classique fibrés, These, Univ. Genève (1981).

    Google Scholar 

  26. E. S. Rapaport, On the commutator subgroup of a knot group. Ann. Math.71, 157–162 (1960).

    Article  MathSciNet  Google Scholar 

  27. K. Reidemeister, Homotopieringe und Linsenraume. Abh. Math. Sem. Univ. Hamburg11, 102–109 (1935).

    Article  MATH  Google Scholar 

  28. D. Rolfsen, Knots and Links. Berkeley, Publish or Perish, Inc. (1976).

    MATH  Google Scholar 

  29. H. Schubert, Knoten mit zwei Brücken. Math. Z.65, 133–170 (1965).

    Article  MathSciNet  Google Scholar 

  30. H. Seifert, Über das Geschlecht von Knoten. Math. Ann.110, 571–592 (1934).

    Article  MathSciNet  Google Scholar 

  31. Y. Shinohara, On the signature of a link with two bridges. Kwansei, Gakuin, Univ. Annual Stud.25, 111–119 (1976).

    MathSciNet  Google Scholar 

  32. L. Siebenmann, Exercises sur les noeuds rationnels. Polycopié, Orsay (1975).

    Google Scholar 

  33. H. Zieschang, Classification of Montesinos knots (1983).

  34. H. Zieschang, E. Vogt, H.-D. Coldewey, Flachen und ebene diskontinuierliche Gruppen. Lecture Notes in Math.122, Berlin, Springer-Verlag (1970).

    Google Scholar 

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  1. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, Frankfurt am Main, Postfach 111932, D-6000, Frankfurt am Main

    Gerhard Von Burde

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  1. Gerhard Von Burde
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Von Burde, G. Über das geschlecht und die faserbarkeit von montesinos-knoten. Abh.Math.Semin.Univ.Hambg. 54, 199–226 (1984). https://doi.org/10.1007/BF02941452

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