On nonsimple 3-manifolds and 2-handle addition

DOI10.1016/0166-8641(94)90114-7zbMath0816.57014OpenAlexW1965231434MaRDI QIDQ1313927

Mario Eudave-Muñoz

Publication date: 20 July 1995

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0166-8641(94)90114-7

zbMATH Keywords

tunnel number one knots2-handle additioncompressible boundaryessential annulus and torusnonsimple 3-manifold

Mathematics Subject Classification ID

Related Items (19)

Knots of tunnel number one and meridional tori ⋮ Obtaining genus 2 Heegaard splittings from Dehn surgery ⋮ Classification of genus two knots which admit a \((1,1)\)-decomposition ⋮ Double branched covers of tunnel number one knots ⋮ Hyperbolicity of the canonical genus two knots ⋮ Non-simple links with tunnel number one ⋮ Primitive, proper power, and Seifert curves in the boundary of a genus two handlebody ⋮ HYPERBOLIC KNOTS WITH THREE TOROIDAL DEHN SURGERIES ⋮ Composite tunnel number one genus two handlebody-knots ⋮ Comparing 2-handle additions to a genus 2 boundary component ⋮ Unnamed Item ⋮ Genus one knots which admit (1,1)-decompositions ⋮ Two-Generator Cable Knots are Tunnel One ⋮ Seifert surfaces for genus one hyperbolic knots in the 3-sphere ⋮ Knots and surfaces ⋮ There are no unexpected tunnel number one knots of genus one ⋮ Computing genera of satellite tunnel number one knots and torti-rational knots ⋮ Derivation of Schubert normal forms of 2-bridge knots from (1,1)-diagrams ⋮ INCOMPRESSIBLE SURFACES AND (1, 1)-KNOTS

Cites Work

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• Incompressibility of surfaces after Dehn surgery
• On unknotting tunnels for knots
• Tunnel number one knots satisfy the Poenaru conjecture
• Surfaces incompressibles dans les variétés obtenues par chirurgie longitudinale le long d'un noeud de \(S^ 3\)
• Reducing Heegaard splittings
• On primitive sets of loops in the boundary of a handlebody
• Dehn Surgery and Satellite Knots
• Adding a 2-Handle to a 3-Manifold: An Application to Property R
• The Thurston Norm and 2-Handle Addition
• Every Two-Generator Knot is Prime
• Simple Knots in Compact, Orientable 3-Manifolds
• Dehn surgery on knots

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