Vol. 110, No. 2, 1984

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Atoroidal, irreducible 3-manifolds and 3-fold branched coverings of S3

Teruhiko Soma

Vol. 110 (1984), No. 2, 435–446
Abstract

Suppose M is a closed orientable 3-manifold. Then H. Hilden et al. proved that M is a 3-fold branched covering of S3 branched over a fibered knot. In this paper we prove that, if M is irreducible and atoroidal, then M is either a 3-fold branched covering of S3 branched over a simple, fibered knot, or a 2-fold branched covering of a closed orientable 3-manifold whose Heegaard genus is at most one.

Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57M12
Milestones
Received: 1 June 1982
Revised: 22 November 1982
Published: 1 February 1984
Authors
Teruhiko Soma
Department of Mathematics and Information Sciences
Tokyo Metropolitan University
Minami-Ohsawa 1-1, Hachioji
Tokyo 192-0397
Japan