Knotted homology 3-spheres in S5

Osamu SAEKI

doi:10.2969/jmsj/04010065

Knotted homology 3-spheres in S⁵

Osamu SAEKI

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JOURNAL FREE ACCESS

1988 Volume 40 Issue 1 Pages 65-75

DOI https://doi.org/10.2969/jmsj/04010065

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Published: 1988 Received: June 30, 1986 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) E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math., 2 (1966), 1-14.
2) W. Browder and J. Levine, Fibering manifolds over a circle, Comment. Math. Helv., 40 (1966), 153-160.
3) J. W. Cannon, Shrinking cell-like decompositions of manifolds: Codimension three, Ann, of Math., 110 (1979), 83-112.
4) S. Donaldson, An application of gauge theory to 4-dimensional topology, J. Differential Geom., 18 (1983), 279-315.
5) A. Durfee, Fibered knots and algebraic singularities, Topology, 13 (1974), 47-59.
6) R. D. Edwards, The double suspension of a certain homology 3-sphere is S⁵, Notices Amer. Math. Soc., 22 (1975), Abstract #75 T-G33.
7) J. A. Hillman, Simple locally flat 3-knots, Bull. London Math. Soc., 16 (1984), 599-602.
8) F. Hirzebruch, W. D. Neumann and S. S. Koh, Differentiable manifolds and quadratic forms, Marcel Dekker, New York, 1971.
9) C. Kearton, Some non-fibered 3-knots, Bull. London Math. Soc., 15 (1983), 365-367.
10) J. Levine, Unknotting spheres in codimension two, Topology, 4 (1965), 9-16.
11) J. Levine, Polynomial invariants of knots of codimension two, Ann, of Math., 84 (1966), 537-554.
12) J. Levine, An algebraic classification of some knots of codimension two, Comment. Math. Helv., 45 (1970), 185-198.
13) F. Michel and C. Weber, Noeuds algébriques décomposables, C. R. Acad. Sci. Paris Sér. A-B, 294 (1982), 493-496.
14) J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Stud., 61, Princeton Univ. Press, Princeton, 1968.
15) D. Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Publ. Math. IHES., 9(1961), 5-22.
16) W. D. Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc., 268 (1981), 299-344.
17) S. Plotnick, Embedding homology 3-spheres in S⁵, Pacific J. Math., 101 (1982), 147-151.
18) O. Saeki, On simple fibered knots in S⁵ and the existence of decomposable algebraic 3-knots, to appear in Comment. Math. Helv..
19) M. Scharlemann, Non-PL imbeddings of 3-manifolds, Amer. J. Math., 100 (19781 539-545.
20) J. Stallings, On fibering certain 3-manifolds, Topology of 3-Manifolds and Related Topics, Prentice-Hall, New Jersey, 1962, pp. 95-100.
21) B. L. van der Waerden, Moderne Algebra, vol. 1, Springer, 1930.

Right : [1] E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math., 2 (1966), 1-14.
[2] W. Browder and J. Levine, Fibering manifolds over a circle, Comment. Math. Helv., 40 (1966), 153-160.
[3] J. W. Cannon, Shrinking cell-like decompositions of manifolds: Codimension three, Ann, of Math., 110 (1979), 83-112.
[4] S. Donaldson, An application of gauge theory to 4-dimensional topology, J. Differential Geom., 18 (1983), 279-315.
[5] A. Durfee, Fibered knots and algebraic singularities, Topology, 13 (1974), 47-59.
[6] R. D. Edwards, The double suspension of a certain homology 3-sphere is S⁵, Notices Amer. Math. Soc., 22 (1975), Abstract #75 T-G33.
[7] J. A. Hillman, Simple locally flat 3-knots, Bull. London Math. Soc., 16 (1984), 599-602.
[8] F. Hirzebruch, W. D. Neumann and S. S. Koh, Differentiable manifolds and quadratic forms, Marcel Dekker, New York, 1971.
[9] C. Kearton, Some non-fibered 3-knots, Bull. London Math. Soc., 15 (1983), 365-367.
[10] J. Levine, Unknotting spheres in codimension two, Topology, 4 (1965), 9-16.
[11] J. Levine, Polynomial invariants of knots of codimension two, Ann, of Math., 84 (1966), 537-554.
[12] J. Levine, An algebraic classification of some knots of codimension two, Comment. Math. Helv., 45 (1970), 185-198.
[13] F. Michel and C. Weber, Noeuds algébriques décomposables, C. R. Acad. Sci. Paris Sér. A-B, 294 (1982), 493-496.
[14] J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Stud., 61, Princeton Univ. Press, Princeton, 1968.
[15] D. Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Publ. Math. IHES., 9 (1961), 5-22.
[16] W. D. Neumann, A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves, Trans. Amer. Math. Soc., 268 (1981), 299-344.
[17] S. Plotnick, Embedding homology 3-spheres in S⁵, Pacific J. Math., 101 (1982), 147-151.
[18] O. Saeki, On simple fibered knots in S⁵ and the existence of decomposable algebraic 3-knots, to appear in Comment. Math. Helv..
[19] M. Scharlemann, Non-PL imbeddings of 3-manifolds, Amer. J. Math., 100 (1978) 539-545.
[20] J. Stallings, On fibering certain 3-manifolds, Topology of 3-Manifolds and Related Topics, Prentice-Hall, New Jersey, 1962, pp. 95-100.
[21] B. L. van der Waerden, Moderne Algebra, vol. 1, Springer, 1930.

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