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Some cobordism invariants for links

Published online by Cambridge University Press:  24 October 2008

A. G. Tristram
A. G. Tristram
Affiliation:
Churchill College, Cambridge
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Extract

The purpose of this paper is to obtain some necessary conditions for a link in Euclidean 3-space to be spanned by a locally unknotted surface of given type in one half of 4-space. In particular necessary conditions for two links to be cobordant are proved.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 251 - 264
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Andrews, J. J. and Dristy, F.The Minkowski units of ribbon knots. Proc. Amer. Math. Soc. 15 (1964), 856–864.CrossRefGoogle Scholar
(2)Fox, R. H.A quick trip through knot theory. Topology of 3-manifolds Symposium (Prentice-Hall, 1962), 120–176.Google Scholar
(3)Hosokawa, F. and Yanagawa, T.Is every slice knot a ribbon knot? Osaka J. Math. 2 (1965), 373–384.Google Scholar
(4)Hudson, J. F. P. and Zeeman, E. C.On regular neighbourhoods. Proc. London Math. Soc. 14 (1964), 719–745.Google Scholar
(5)Hudson, J. F. P. and Zeeman, E. C.On combinatorial isotopy. Inst. Hautes Etudes Sci. Publ. Math. 19 (1964), 69–94.CrossRefGoogle Scholar
(6)Kervaire, M. and Milnor, J.On 2-spheres in 4-manifolds. Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 1651–1657.CrossRefGoogle ScholarPubMed
(7)Lashof, R.Problems in differential and algebraic topology. Seattle Conference, 1963. Ann. of Math. 81 (1965), 565–591.CrossRefGoogle Scholar
(8)Murasugi, K.On the Minkowski unit of slice links. Trans. Amer. Math. Soc. 114 (1965), 377–383.CrossRefGoogle Scholar
(9)Murasugi, K.On a certain numerical invariant of link types. Trans. Amer. Math. Soc. 11 (1965), 387–422.CrossRefGoogle Scholar
(10)Reidemeister, K.Knotentheorie (Ergebnisse der Mathematik und ihrer Grenzgebiete, 1·1. Springer: Berlin, 1932).Google Scholar
(11)Tristram, A. G.On the equivalence of the bilinear forms for equivalent and ribbon equivalent links: mimeographed notes, D.P.M.M.S., Cambridge University, England, 1969.Google Scholar
(12)Zeeman, E. C.Seminar on Combinatorial Topology: mimeographed notes, Inst. des Hautes Etudes Sci. (Paris, 1963).Google Scholar