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

DOI: 10.2140/pjm.1976.65.65

Abstract

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

Milestones

Received: 7 April 1975

Revised: 4 November 1975

Published: 1 July 1976