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On spanning surfaces of links

Published online by Cambridge University Press:  17 April 2009

J.F.P. Hudson
J.F.P. Hudson
Affiliation:
School of Mathematics and Information Sciences, Massey University, Private Bag Palmerston North, New Zealand
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In his paper on knot cobordism groups in codimension 2, Levine develops conditions for a knotted Sn in Sn+2 to bound a disc in Bn+3 In this paper some of his methods are extended to introduce a necessary condition for a classical link in S3 to bound a surface of specified genus in B4. In particular, this answers a question of Zeemann's about some links related to the ‘Mazur link’.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 337 - 345
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Levine, J., ‘Knot cobordism groups in codimension 2’, Comment. Math. Helv. 42 (1969), 229–244.CrossRefGoogle Scholar
[2]Tristram, A.G., ‘Some cobordism invariants for links’, Proc. Camb. Phil. Soc. 66 (1969), 351–264.CrossRefGoogle Scholar
[3]Murasugi, K., ‘On a certain link invariant of link types’, Trans. Amer. Math. Soc. 114 (1965), 377–383.CrossRefGoogle Scholar