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

Teruhiko Soma

Vol. 110 (1984), No. 2, 435–446

DOI: 10.2140/pjm.1984.110.435

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