On Heegaard decompositions of torus knot exteriors and related Seifert fibre spaces

DOI10.1007/BF01456287zbMath0616.57008MaRDI QIDQ1821389

Heiner Zieschang, Markus Rost, Michel Boileau

Publication date: 1988

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164340

zbMATH Keywords

Heegaard decompositionSeifert fibre spacesexterior of a knotHeegaard decompositions of genus 2 of torus knot exteriorsNielsen equivalence classes of one relator presentations of the fundamental groups

Mathematics Subject Classification ID

Related Items (36)

ALEXANDER QUANDLE LOWER BOUNDS FOR LINK GENERA ⋮ Heegaard splittings and branched coverings of B 3 ⋮ Iterated splitting and the classification of knot tunnels ⋮ Unknotting tunnels in hyperbolic 3-manifolds ⋮ Tunnel Numbers of Knots ⋮ Unnamed Item ⋮ Heegaard splittings of Seifert fibered spaces ⋮ A criterion for detecting inequivalent tunnels for a knot ⋮ Double branched covers of tunnel number one knots ⋮ Torus knots obtained by twisting torus knots ⋮ Generalized torsion for hyperbolic 3‐manifold groups with arbitrary large rank ⋮ Tunnel complexes of 3-manifolds ⋮ Middle tunnels by splitting ⋮ Uniqueness of higher genus bridge surfaces for torus knots ⋮ On unknotting tunnels for knots ⋮ Some bounds for the regular genus of PL-manifolds ⋮ Non-simple links with tunnel number one ⋮ Examples of tunnel number one knots which have the property ‘1 + 1 = 3’ ⋮ STABILIZING HEEGAARD SPLITTINGS OF COMPOSITE TUNNEL NUMBER TWO KNOTS ⋮ Primitive, proper power, and Seifert curves in the boundary of a genus two handlebody ⋮ A complete invariant for closed surfaces in the three-sphere ⋮ Heegaard splittings and homeotopy groups of small Seifert fibre spaces ⋮ TWISTED TORUS KNOTS T(p, q; 3, s) ARE TUNNEL NUMBER ONE ⋮ Common stabilizations of Heegaard splittings of link exteriors ⋮ Knots and surfaces ⋮ There are Knots whose Tunnel Numbers go down under Connected Sum ⋮ Cabling sequences of tunnels of torus knots ⋮ Tunnel leveling, depth, and bridge numbers ⋮ The topology, geometry and algebra of unknotting tunnels ⋮ Unknotting annuli and handlebody-knot symmetry ⋮ Small Seifert-fibered Dehn surgery on hyperbolic knots ⋮ Tunnel-number-one knot exteriors in \(S^3\) disjoint from proper power curves ⋮ COMPUTING MATVEEV'S COMPLEXITY VIA CRYSTALLIZATION THEORY: THE BOUNDARY CASE ⋮ ON TANGLE DECOMPOSITIONS OF TWISTED TORUS KNOTS ⋮ On boundary primitive manifolds and a theorem of Casson--Gordon ⋮ Genus 2 Heegaard decompositions of small Seifert manifolds

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