The support of global graph links

Koichi YANO

doi:10.2969/jmsj/03740683

Koichi YANO

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JOURNAL FREE ACCESS

1985 Volume 37 Issue 4 Pages 683-702

DOI https://doi.org/10.2969/jmsj/03740683

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Published: 1985 Received: April 27, 1984 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: CITATION Details: Wrong : 1) D. Asimov, Round handles and non-singular Morse-Smale flows, Ann. of Math., 102 (1975), 41-54.
2) R. H. Bing, Necessary and sufficient conditions that a 3-manifold be S³, Ann. of Math., 69 (1958), 17-37.
3) D. Eisenbud and W. D. Neumann, Graph links, preprint.
4) C. McA. Gordon, Dehn surgery and satellite knots, Trans. Amer. Math. Soc., 275 (1983), 687-708.
5) A. E. Hatcher, On the boundary curves of incompressible surfaces, Pacific J. Math., 99 (1982), 373-377.
6) J. Hempel, 3-manifolds, Ann. of Math. Studies, 86, Princeton Univ. Press, Princeton, New Jersey, 1976.
7) W. H. Jaco and P. B. Shalen, Seifert fibred spaces in 3-manifolds, Mem. Amer. Math. Soc., 21, 1979.
8) K. Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Math., 761, Springer-Verlag, 1979.
9) H. Kneser, Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten, Jber. Deutsch. Math.-Verein., 38 (1929), 248-260.
10) J. Milnor, A unique factorization theorem for 3-manifolds, Amer. J. Math., 79 (1962), 1-7.
11) J. Morgan, Non-singular Morse-Smale flows on 3-dimensional manifolds, Topology, 18 (1978), 41-53.
12) W. D. Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc., 267 (1981), 299-344.
13) T. Soma, The Gromov invariant of links, Invent. Math., 64 (1981), 445-454.
14) I. Tamura, Unknotted codimension one spheres in smooth manifolds, Topology, 23 (1984), 127-132.
15) I. Tamura, Fundamental theorems in global knot theory, preprint.
16) W. P. Thurston, The geometry and topology of 3-manifolds, Princeton Mimeographed Note, 1977-1978.
17) W. P. Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc., 6(1982), 357-381.
18) M. Ue, Some remarks on Dehn surgery along graph knots, J. Fac. Sci. Univ. Tokyo Sect. IA, 30 (1983), 333-352.
19) F. Waldhausen, Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I; II, Invent. Math., 3 (1967), 308-333; 4 (1967), 87-117.
20) K. Yano, The support of global graph links, Proc. Japan Acad. Ser. A, 60 (1984), 70-73.
21) K. Yano, Quasi-localness and unknotting theorems for knots in 3-manifolds, preprint.

Right : [1] D. Asimov, Round handles and non-singular Morse-Smale flows, Ann. of Math., 102 (1975), 41-54.
[2] R. H. Bing, Necessary and sufficient conditions that a 3-manifold be S³, Ann. of Math., 69 (1958), 17-37.
[3] D. Eisenbud and W. D. Neumann, Graph links, preprint.
[4] C. McA. Gordon, Dehn surgery and satellite knots, Trans. Amer. Math. Soc., 275 (1983), 687-708.
[5] A. E. Hatcher, On the boundary curves of incompressible surfaces, Pacific J. Math., 99 (1982), 373-377.
[6] J. Hempel, 3-manifolds, Ann. of Math. Studies, 86, Princeton Univ. Press, Princeton, New Jersey, 1976.
[7] W. H. Jaco and P. B. Shalen, Seifert fibred spaces in 3-manifolds, Mem. Amer. Math. Soc., 21, 1979.
[8] K. Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Math., 761, Springer-Verlag, 1979.
[9] H. Kneser, Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten, Jber. Deutsch. Math. -Verein., 38 (1929), 248-260.
[10] J. Milnor, A unique factorization theorem for 3-manifolds, Amer. J. Math., 79 (1962), 1-7.
[11] J. Morgan, Non-singular Morse-Smale flows on 3-dimensional manifolds, Topology, 18 (1978), 41-53.
[12] W. D. Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc., 267 (1981), 299-344.
[13] T. Soma, The Gromov invariant of links, Invent. Math., 64 (1981), 445-454.
[14] I. Tamura, Unknotted codimension one spheres in smooth manifolds, Topology, 23 (1984), 127-132.
[15] I. Tamura, Fundamental theorems in global knot theory, preprint.
[16] W. P. Thurston, The geometry and topology of 3-manifolds, Princeton Mimeographed Note, 1977-1978.
[17] W. P. Thurston, Three dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc., 6 (1982), 357-381.
[18] M. Ue, Some remarks on Dehn surgery along graph knots, J. Fac. Sci. Univ. Tokyo Sect. IA, 30 (1983), 333-352.
[19] F. Waldhausen, Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I; II, Invent. Math., 3 (1967), 308-333; 4 (1967), 87-117.
[20] K. Yano, The support of global graph links, Proc. Japan Acad. Ser. A, 60 (1984), 70-73.
[21] K. Yano, Quasi-localness and unknotting theorems for knots in 3-manifolds, preprint.

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