Twisting and knot types

Masaharu KOUNO; Kimihiko MOTEGI; Tetsuo SHIBUYA

doi:10.2969/jmsj/04420199

Masaharu KOUNO, Kimihiko MOTEGI, Tetsuo SHIBUYA

著者情報

ジャーナルフリー

1992 年 44 巻 2 号 p. 199-216

DOI https://doi.org/10.2969/jmsj/04420199

詳細

Published: 1992 Received: 1991/03/06 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Department of Mathematics College of Liberal Arts Kobe University
2) Department of Mathematics Kyushu University
3) Department of Mathematics Osaka Institue of Technology

訂正後 :
1) Department of Mathematics College of Liberal Arts Kobe University
2) Department of Mathematics Kyushu University
3) Department of Mathematics Osaka Institute of Technology

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) S. Bleiler and M. Scharlemann, Tangles, Propert P, and a Problem of J. Martin Math. Ann., 273 (1986), 215-225.
2) D. Gabai, Surgery on knots in solid tori, Topology, 28 (1989), 1-6.
3) W. Jaco, Lectures on three manifold topology, Conference board of Math. Science, Regional Conference Series in Math., 43, Amer. Math. Soc., 1980.
4) W. Jaco and P. Shalen, Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc., 220 (1979).
5) K. Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Math., 761, Springer-Verlag, 1979.
6) T. Kanenobu, Examples on polynomial invariants of knots and links, Math. Ann., 275 (1986), 555-572.
7) R. Kirby, Problems in low-dimensional manifold theory, Proc. Symp. Pure Math., 32 (1978), 273-312.
8) M. Kouno, On knots with companions, Kobe J. Math., 2 (1985), 143-148.
9) R. Litherland, Surgery on knots in solid tori, Proc. London Math. Soc., 39 (1979), 130-146.
10) Y. Mathieu, Thesis, L'Université de Provence, 1990.
11) J. Morgan and H. Bass, The Smith conjecture, Pure and Applied Math. Academic Press, 1984.
12) K. Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc., 117 (1965), 387-422.
13) Y. Nakanishi, Prime links, concordance and Alexander invariants, Math. Sem. Notes Kobe Univ., 8 (1980), 561-568.
14) D. Rolfsen, Knots and links, Mathematics Lecture Series, No. 7 Publish or Perish, Barkeley, Calif., 1976.
15) H. Schubert, Knoten and Vollringe, Acta Math., 90 (1953), 131-286.
16) T. Shibuya, On the cobordism of compound knots which are T-congruent, Kobe J. Math., 2 (1985), 71-74.
17) T. Soma, On preimage knots in S³, Proc. Amer. Math. Soc., 100 (1987), 589-592.
18) W. Thurston, The geometry and topology of 3-manifolds, Lecture Note, Princeton Univ., 1978,
19) F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math., 87 (1962), 56-88.
20) J. H. C. Whitehead, On doubled knots, J. London Math. Soc., 12 (1937), 63-71.
21) Y. Yokota, Twisting formulas of the Jones polynomial, Math. Proc. Camb. Phil. Soc., 110 (1991), 473-482.

Right : [1] S. Bleiler and M. Scharlemann, Tangles, Propert P, and a Problem of J. Martin Math. Ann., 273 (1986), 215-225.
[2] D. Gabai, Surgery on knots in solid tori, Topology, 28 (1989), 1-6.
[3] W. Jaco, Lectures on three manifold topology, Conference board of Math. Science, Regional Conference Series in Math., 43, Amer. Math. Soc., 1980.
[4] W. Jaco and P. Shalen, Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc., 220 (1979).
[5] K. Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Math., 761, Springer-Verlag, 1979.
[6] T. Kanenobu, Examples on polynomial invariants of knots and links, Math. Ann., 275 (1986), 555-572.
[7] R. Kirby, Problems in low-dimensional manifold theory, Proc. Symp. Pure Math., 32 (1978), 273-312.
[8] M. Kouno, On knots with companions, Kobe J. Math., 2 (1985), 143-148.
[9] R. Litherland, Surgery on knots in solid tori, Proc. London Math. Soc., 39 (1979), 130-146.
[10] Y. Mathieu, Thesis, L'Université de Provence, 1990.
[11] J. Morgan and H. Bass, The Smith conjecture, Pure and Applied Math. Academic Press, 1984.
[12] K. Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc., 117 (1965), 387-422.
[13] Y. Nakanishi, Prime links, concordance and Alexander invariants, Math. Sem. Notes Kobe Univ., 8 (1980), 561-568.
[14] D. Rolfsen, Knots and links, Mathematics Lecture Series, No. 7 Publish or Perish, Barkeley, Calif., 1976.
[15] H. Schubert, Knoten and Vollringe, Acta Math., 90 (1953), 131-286.
[16] T. Shibuya, On the cobordism of compound knots which are T-congruent, Kobe J. Math., 2 (1985), 71-74.
[17] T. Soma, On preimage knots in S³, Proc. Amer. Math. Soc., 100 (1987), 589-592.
[18] W. Thurston, The geometry and topology of 3-manifolds, Lecture Note, Princeton Univ., 1978,
[19] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math., 87 (1962), 56-88.
[20] J. H. C. Whitehead, On doubled knots, J. London Math. Soc., 12 (1937), 63-71.
[21] Y. Yokota, Twisting formulas of the Jones polynomial, Math. Proc. Camb. Phil. Soc., 110 (1991), 473-482.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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