Morimoto--Sakuma--Yokota's geometric approach to tunnel number one knots

DOI10.1016/S0166-8641(02)00100-1zbMath1018.57003OpenAlexW2026259872MaRDI QIDQ1868864

Hyun Jong Song

Publication date: 28 April 2003

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

Full work available at URL: https://doi.org/10.1016/s0166-8641(02)00100-1

zbMATH Keywords

Montesinos knotsHeegaard decomposition\(\theta\)-curve\({\mathbb Z}_2 \oplus {\mathbb Z}_2\)-branched coveringTunnel number one knot

Mathematics Subject Classification ID

General geometric structures on low-dimensional manifolds (57M50) Relations of low-dimensional topology with graph theory (57M15)

Related Items (1)

UNKNOTTING TUNNELS FOR P(-2,3,7)

Cites Work

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• Identifying tunnel number one knots
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• On unknotting tunnels for knots
• Constructions of two-fold branched covering spaces
• Heegard splittings of prime 3-manifolds are not unique
• Two-generator discrete subgroups of \(\text{Isom}(\mathbb{H}^2)\) containing orientation-reversing elements
• On hyperbolic knots with the same \(m\)-fold and \(n\)-fold cyclic branched coverings
• Heegaard structures of negatively curved 3-manifolds
• On \(\pi\)-hyperbolic knots with the same 2-fold branched coverings
• On involutions of the 3-sphere
• Seifert manifolds
• Genus two Heegaard splittings of exteriors of 1-genus 1-bridge knots
• The Alexander module of a knotted theta-curve
• Heegaard Splittings of Branched Coverings of S 3
• Homology of Abelian Coverings of Links and Spatial Graphs
• Examples of tunnel number one knots which have the property ‘1 + 1 = 3’
• 3-manifolds as viewed from the curve complex

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