References
F. Bonahon,Involutions et Fibrès de Seifert dans les Variétés de Dimensions 3, thesis de 3-ieme cycle, Orsay, France, 1979.
R. Crowell,Genus of Alternating Link Types.Ann. of Math. (2)69 (1959), 258–275.
R. Crowell andH. Trotter,A Class of Pretzel Knots,Duke Math. J.,30 (1963), 373–377.
J. Eisner,Knots with infinitely many minimal Spanning Surfaces,Trans. AMS. 229 (1977), 329–349.
D. Gabai,Foliations and Genera of Links, Thesis, Princeton University, 1980.
———,The Murasugi Sum is a Natural Geometric Operation, Low Dimensional Topology,Cont. Math. AMS20 (1983), 131–144.
———,The Murasugi Sum is a Natural Geometric Operation II, Cont. Math. AMS44 (1985), 93–100.
———,Foliations and Genera of Links, Topology 23 (1984), 381–394.
———,Foliations and the Topology of 3-Manifolds, J. Diff. Geom. 18 (1983), 445–503.
---,Genera of the Alternating Links, to appear in theDuke Math. J.
---,Genera of the Arborescent Links, Memoirs of the AMS, No.339 (1986).
S. Goodman andG. Tavares,Pretzel-Fibred Links, Preprint.
J. Harer,Representing Elements of π1(M3)by Fibred Knots,Math. Proc. Cambridge Phil. Soc.,92 (1982), 133–138.
T. Kanenabu,The Augmentation Subgroup of a Pretzel Link,Math. Seminar Notes, Kobe University,7 (1979), 363–384.
S. Kinoshita andTerasaka,On Unions of Knots, Osaka Math. J. 1957, 131–153.
H. R. Morton,Fibred Knots with a given Alexander Polynomial, Preprint.
K. Murasugi,On the Genus of the Alternating Knot I,II J. Math. Soc. of Japan,10 (1958), 94–105, 235–248.
———,On a Certain Subgroup of an Alternating Link, Amer. J. Math., 85 (1963), 544–550.
L. P. Neuwirth,Knot Groups, Annals of Math. Studies, 56, Princeton University Press (1965).
U. Oertel,Aborescent Links, Thesis, University of California, Los Angeles, 1980.
R. Parris,Pretzel Knots, Thesis, Princeton University, 1978.
D. Rolfsen,Knots and Links, Publish or Perish 1977.
G. H. Reeb,Sur Certaines Proprietes Topologiques des Variétés Feuilletées, Actualités Sci. Indust., No. 1183, Hermann, Paris (1952), 91–158.
R. Roussarie,Plongements dans les Variétés Feuilletées et Classification de Feuilletages sans Holonomie, IHES Publ. Math. No.443 (1973) 101–142.
T. Soma,Hyperbolic Fibred Links and Fibre Concordences,Math. Proc. Cambridge Phil. Soc.,96 (1984), 283–294.
J. Stallings,On Fibering Certain 3-Manifolds, Topology of 3-Manifolds, Prentice Hall (1962), 95–100.
———,Constructions of Fibred Knots and Links, Proc. Symp. Pure Math. AMS27 (1975), 315–319.
W. P. Thurston,On the Geometry and Dynamics of Diffeomorphisms of Surfaces I, preprint.
———,Three dimensional Manifolds, Kleinian Groups, and Hyperbolic Geometry, Proc. Symp. Pure Math. AMS39 (1983), 87–114.
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Partially supported by grants from the National Science foundation.
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Gabai, D. Detecting fibred links inS 3 . Commentarii Mathematici Helvetici 61, 519–555 (1986). https://doi.org/10.1007/BF02621931
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DOI: https://doi.org/10.1007/BF02621931