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The first author [Amer. J. Math. 98 (1976), no. 4, 989–992] and the second author [Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 85–94] have shown that any closed orientable 3-manifold M is a 3-fold cover of S3 branched over a knot. In the present paper it is proved that matters may be arranged so that the curve in M which covers the branch set in S3 bounds a disc in M.

Closed oriented 3-manifolds as 3-fold branched coverings ofS3of special type

Closed oriented 3-manifolds as 3-fold branched coverings ofS³of special type