Vol. 65, No. 1, 1976

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Closed oriented 3-manifolds as 3-fold branched coverings of S3 of special type

Hugh M. Hilden, José M. Montesinos and Thomas Lusk Thickstun

Vol. 65 (1976), No. 1, 65–76

It has been shown by Hilden and Montesinos independently that any closed oriented 3-manifold M is a 3-fold irregular branched covering of S3, p : M S3. The purpose of this paper is to show that the branch covering space map can be chosen in such a way that the set of points at which p fails to be a local homeomorphism is the boundary of a disc in M. One application of this result is a new proof that a closed oriented 3-manifold is parallelizable.

Mathematical Subject Classification
Primary: 57A10, 57A10
Secondary: 55A10
Received: 7 April 1975
Revised: 4 November 1975
Published: 1 July 1976
Hugh M. Hilden
José M. Montesinos
Thomas Lusk Thickstun