Small knots in Seifert fibered 3-manifolds
type: Item
instance of: scholarly article
title: Small knots in Seifert fibered 3-manifolds
zbMATH Open document ID: 0789.57009
DOI: 10.1007/BF02571644
author: V. Pereyra
published in: Mathematische Zeitschrift
publication date: 1994-06-14T00:00:00Z
full work available at URL: https://eudml.org/doc/174475
review text: Constructing knots with given properties in arbitrary 3-manifolds turns out to be a rather difficult problem. The question we consider here is: at which conditions does an arbitrary 3-manifold contain a small knot, i.e. a knot without closed incompressible surfaces in its exterior excepted peripheral tori? Actually one can hope that such knots exist at least in non-Haken 3-manifolds; this may be interesting in this case since such knots have a property which is very close to the one possessed by the ambient manifold. In this paper we prove that non-trivial small knots exist in non-Haken Seifert fibered 3-manifolds (by non-trivial knots we mean knots that are not fibers of the Seifert fibration).
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 549741
zbMATH Keywords: knot without closed incompressible surfaces in its exterior
zbMATH Keywords: non-Haken Seifert fibered 3-manifolds
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 549741