Knot surgery and primeness

DOI10.1017/S0305004100063969zbMath0591.57002MaRDI QIDQ3719497

Hamish Short, Francisco González-Acuña

Publication date: 1986

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

Alexander polynomialhomotopy 3-spheretorus knotcable knotsprime manifoldsdouble branched cover of \(S^ 3\)homology primehomotopy primenon-prime 3-manifoldssurgeries on knots in \(S^ 3\)surgeries on two-bridge knots

Mathematics Subject Classification ID

Related Items (38)

Networking Seifert Surgeries on Knots ⋮ Reducible surgery in lens spaces and seiferters ⋮ Heegaard Floer groups of Dehn surgeries ⋮ On proper powers in free products and Dehn surgery ⋮ The genus problem for one-relator products of locally indicable groups ⋮ Banding, twisted ribbon knots, and producing reducible manifolds via Dehn surgery ⋮ Exceptional surgeries in 3-manifolds ⋮ Dehn surgery on knots—tracing the evolution of research ⋮ Exceptional surgeries on \((-2,p,p)\)-pretzel knots ⋮ \(H(2)\)-unknotting operation related to 2-bridge links ⋮ Maximal Thurston–Bennequin number and reducible Legendrian surgery ⋮ Knots with the lens space surgery ⋮ Exceptional surgeries on knots with exceptional classes ⋮ A cabling conjecture for knots in lens spaces ⋮ Dehn surgery on knots in solid tori creating essential annuli ⋮ On hyperbolic knots in \(S^3\) with exceptional surgeries at maximal distance ⋮ Exceptional and cosmetic surgeries on knots ⋮ Toroidal Seifert fibered surgeries on alternating knots ⋮ Can Dehn surgery yield three connected summands? ⋮ Comparing 2-handle additions to a genus 2 boundary component ⋮ Dehn surgery on knots ⋮ Dehn surgery on crosscap number two knots and projective planes ⋮ Contact structures and reducible surgeries ⋮ Multibranched surfaces in 3-manifolds ⋮ Knots and surfaces ⋮ All exceptional surgeries on alternating knots are integral surgeries ⋮ The strong slope conjecture for cablings and connected sums ⋮ Isolated exceptional Dehn surgeries on hyperbolic knots ⋮ Seifert-fibered surgeries which do not arise from primitive/Seifert-fibered constructions ⋮ Small Seifert-fibered Dehn surgery on hyperbolic knots ⋮ Characterization of 3-punctured spheres in non-hyperbolic link exteriors ⋮ Essential surfaces of non-negative Euler characteristic in genus two handlebody exteriors ⋮ Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot ⋮ All integral slopes can be Seifert fibered slopes for hyperbolic knots ⋮ Producing essential 2-spheres ⋮ Spelling theorems and Cohen-Lyndon theorems for one-relator products ⋮ Symmetric knots and the cabling conjecture ⋮ A proof of the Scott-Wiegold conjecture on free products of cyclic groups

Cites Work

• Incompressible planar surfaces in 3-manifolds
• Constructing lens spaces by surgery on knots
• Splitting the PL involutions of nonprime 3-manifolds
• Roots and centralizers of peripheral elements in knot groups
• Über die Nielsensche Kürzungsmethode in freien Produkten mit Amalgam
• Elementary surgery along a torus knot
• Dehn Surgery and Satellite Knots
• Elementary Surgery Manifolds and the Elementary Ideals
• Every Two-Generator Knot is Prime
• The homeomorphism problem for 𝑆³
• LINKINGS, TWO-SHEETED BRANCHED COVERINGS AND BRAIDS
• On a Certain Subgroup of the Group of an Alternating Link
• Unnamed Item

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