Incompressible punctured tori in the complements of alternating knots
type: Item
instance of: scholarly article
title: Incompressible punctured tori in the complements of alternating knots
zbMATH Open document ID: 0817.57013
DOI: 10.1007/BF01446618
author: Robert M. Patton
published in: Mathematische Annalen
publication date: 1995-07-31T00:00:00Z
full work available at URL: https://eudml.org/doc/165280
review text: The alternating knots which allow an incompressible, boundary incompressible, punctured torus to be properly imbedded in their complements are determined to be the 2-bridge knots which have a continued fraction expansion of length two and the pretzel knots. All of the incompressible tori can be explicitly seen. For 2-bridge knots, the manifolds obtained by performing Dehn surgery on the boundary slopes of these punctured tori are shown to break up along incompressible tori into Seifert-fibred spaces.
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 734578
zbMATH Keywords: alternating knots
zbMATH Keywords: incompressible, boundary incompressible, punctured torus
zbMATH Keywords: 2-bridge knots
zbMATH Keywords: continued fraction expansion of length two
zbMATH Keywords: pretzel knots
zbMATH Keywords: Seifert-fibred spaces
MaRDI profile type: Publication
cites work: Boundary slopes for Montesinos knots
cites work: Incompressible surfaces in 2-bridge knot complements
cites work: Closed incompressible surfaces in alternating knot and link complements
cites work: Q3987886
cites work: The classification of alternating links
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description: scientific article; zbMATH DE number 734578