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In his paper on knot cobordism groups in codimension 2, Levine develops conditions for a knotted 5™ in S n+i to bound a disc in B n+3 . In this paper some of his methods are extended to introduce a necessary condition for a classical link in S 3 to bound a surface of specified genus in B*. In particular, this answers a question of Zeemann's about some links related to the 'Mazur link'.doi:10.1017/s0004972700015756 fatcat:ukn2zzgblrbujav6huqrn4ur5q