Genus one fibered knots in lens spaces

Kanji MORIMOTO

doi:10.2969/jmsj/04110081

Kanji MORIMOTO

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JOURNAL FREE ACCESS

1989 Volume 41 Issue 1 Pages 81-96

DOI https://doi.org/10.2969/jmsj/04110081

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Published: 1989 Received: July 27, 1987 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Junzo Tao on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) F. Bonahon et J. P. Otal, Scindements de Heegaard des espace lenticulaires, Ann. Sci. École Norm. Sup., 4^e série, 16 (1983), 451-466.
2) E. J. Brody, The topological classification of the lens spaces, 71 (1960), 163-185.
3) G. Burde and H. Zieschang, Neuwirthsche knoten und Flächenabbildungen, Abh. Math. Sem. Univ. Hamburg, 31 (1967), 239-246.
4) A. J. Casson and C. McA. Gordon, Manifolds with irreducible Heegaard splittings of arbitrarily high genus (to appear).
5) R. H. Crowell and R. H. Fox, Introduction to Knot Theory, Ginn and Co., Boston, Mass., 1963.
6) F. Gonzáles-Acuna, Dehn's constraction on knots, Bol. Soc. Mat. Mexicana, 15 (1970), 58-77.
7) J. Harer, Representing elements of π₁(M³) by fibered knots, Proc. Camb. Soc., 92 (1982), 133-138.
8) J. Hempel, 3-manifolds, Ann. Math. Studies, 86, Princeton N. J., Princeton University Press, 1976.
9) L. Moser, Elementary surgery along a torus knot, Pacific J. Math., 38 (1971), 737-745.
10) D. A. Neumann, 3-manifolds fibering over S¹, Proc. Amer. Math. Soc., 58 (1976), 353-356.
11) M. Ochiai and M. Takahashi, Heegaard diagrams of torus bundles over S¹, Comment. Math. Univ. St. Paul., 31 (1982), 63-69.
12) N. Pecynski, G. Rosenberger und H. Zieschang, Über erzeugende ebener diskontinuierlicher gruppen, Invent. Math., 29 (1975), 161-180.
13) D. Rolfsen, Knots and Links, Math. Lecture Series, 7, Publish or Perish Inc., Berkeley, 1976.
14) F. Waldhausen, Heegaard-zerlegungen der 3-sphäre, Topology, 7 (1968), 195-203.

Right : [1] F. Bonahon et J. P. Otal, Scindements de Heegaard des espace lenticulaires, Ann. Sci. École Norm. Sup., 4^e série, 16 (1983), 451-466.
[2] E. J. Brody, The topological classification of the lens spaces, 71 (1960), 163-185.
[3] G. Burde and H. Zieschang, Neuwirthsche knoten und Flächenabbildungen, Abh. Math. Sem. Univ. Hamburg, 31 (1967), 239-246.
[4] A. J. Casson and C. McA. Gordon, Manifolds with irreducible Heegaard splittings of arbitrarily high genus (to appear).
[5] R. H. Crowell and R. H. Fox, Introduction to Knot Theory, Ginn and Co., Boston, Mass., 1963.
[6] F. Gonzáles-Acuna, Dehn's constraction on knots, Bol. Soc. Mat. Mexicana, 15 (1970), 58-77.
[7] J. Harer, Representing elements of π₁(M³) by fibered knots, Proc. Camb. Soc., 92 (1982), 133-138.
[8] J. Hempel, 3-manifolds, Ann. Math. Studies, 86, Princeton N. J., Princeton University Press, 1976.
[9] L. Moser, Elementary surgery along a torus knot, Pacific J. Math., 38 (1971), 737-745.
[10] D. A. Neumann, 3-manifolds fibering over S¹, Proc. Amer. Math. Soc., 58 (1976), 353-356.
[11] M. Ochiai and M. Takahashi, Heegaard diagrams of torus bundles over S¹, Comment. Math. Univ. St. Paul., 31 (1982), 63-69.
[12] N. Pecynski, G. Rosenberger und H. Zieschang, Über erzeugende ebener diskontinuierlicher gruppen, Invent. Math., 29 (1975), 161-180.
[13] D. Rolfsen, Knots and Links, Math. Lecture Series, 7, Publish or Perish Inc., Berkeley, 1976.
[14] F. Waldhausen, Heegaard-zerlegungen der 3-sphäre, Topology, 7 (1968), 195-203.

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