Lower bounds for the unknotting numbers of certain torus knots
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- by Makoto Yamamoto
- Proc. Amer. Math. Soc. 86 (1982), 519-524
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671228-X
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Abstract:
In this paper we shall show that the unknotting numbers of the $(l,2kl \pm 1)$-torus knots are at least $(k({l^2} - 1) - 2)/2$ for $l$ odd and $(k{l^2} - 2)/2$ for $l$ even, where $l$ is an integer greater than one and $k$ is a positive integer.References
- J. M. Boardman, Some embeddings of 2-spheres in 4-manifolds, Proc. Cambridge Philos. Soc. 60 (1964), 354–356. MR 160241, DOI 10.1017/s0305004100037828
- Michel A. Kervaire and John W. Milnor, On $2$-spheres in $4$-manifolds, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1651–1657. MR 133134, DOI 10.1073/pnas.47.10.1651
- John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0239612
- Kunio Murasugi, On a certain numerical invariant of link types, Trans. Amer. Math. Soc. 117 (1965), 387–422. MR 171275, DOI 10.1090/S0002-9947-1965-0171275-5
- V. A. Rohlin, Two-dimensional submanifolds of four-dimensional manifolds, Funkcional. Anal. i Priložen. 5 (1971), no. 1, 48–60 (Russian). MR 0298684
- Emery Thomas and John Wood, On manifolds representing homology classes in codimension $2$, Invent. Math. 25 (1974), 63–89. MR 383438, DOI 10.1007/BF01389998 S. H. Weintraub, ${Z_p}$-actions and rank of ${H_2}({N^{2n}})$, J. London Math. Soc. (2) 13 (1976), 567-572. —, Inefficiently embedded surfaces in $4$-manifolds, Algebraic Topology Aarhus 1978 (J. L. Dupont and I. H. Madsen, eds.), Lecture Notes in Math., vol. 763, Springer-Verlag, Berlin and New York, 1979.
- W. C. Hsiang and R. H. Szczarba, On embedding surfaces in four-manifolds, Algebraic topology (Proc. Sympos. Pure Math., Vol. XXII, Univ. Wisconsin, Madison, Wis., 1970) Amer. Math. Soc., Providence, R.I., 1971, pp. 97–103. MR 0339239
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 519-524
- MSC: Primary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671228-X
- MathSciNet review: 671228