Atoroidal, irreducible 3-manifolds and 3-fold branched coverings of \(S^ 3\)
type: Item
instance of: scholarly article
title: Atoroidal, irreducible 3-manifolds and 3-fold branched coverings of \(S^ 3\)
zbMATH Open document ID: 0544.57001
author: Teruhiko Soma
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: In the midst of 70's it was shown independently by U. Hirsch, H. Hilden, and J. Montesinos that every closed, connected, orientable 3-manifold M is a 3-fold irregular branched cover of the \(S^ 3\) branched over a knot. Moreover, the knot always may be chosen to be fibered. The author refines these results in the case of irreducible and atoroidal M. Namely, in this case at least one of the following is true: (a) M is a 3-fold (cyclic or irregular) branched cover of \(S^ 3\) branched over a simple, fibered knot; (b) M is a 2-fold (cyclic) branched cover of \(S^ 3\) or \(S^ 1\times S^ 2\) or a lens space branched over a simple link.
Mathematics Subject Classification ID: 57M12
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 3866207
zbMATH Keywords: atoroidal 3-manifolds as branched covers
zbMATH Keywords: 3-fold irregular branched cover of the 3-sphere
zbMATH Keywords: fibered knot
MaRDI profile type: Publication
full work available at URL: pjm.1984.110.435
OpenAlex ID: W2028527466
DOI: 10.2140/PJM.1984.110.435
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description: scientific article; zbMATH DE number 3866207