Unknotting Number One Knots are Prime: A New Proof

DOI10.2307/2048550zbMath0728.57008OpenAlexW4251952520MaRDI QIDQ3352140

Xingru Zhang

Publication date: 1991

Full work available at URL: https://doi.org/10.2307/2048550

zbMATH Keywords

knotsprimeunknotting number

Mathematics Subject Classification ID

Related Items (10)

Knots with unknotting number 1 and essential Conway spheres ⋮ 4-Move distance of knots ⋮ Only single twists on unknots can produce composite knots ⋮ Primeness of Twisted Knots ⋮ Links with Unlinking Number One are Prime ⋮ Dehn surgery on knots ⋮ Crossing changes ⋮ Unknotting operations on knots and links ⋮ Lernaean knots and band surgery ⋮ The Montesinos trick for proper rational tangle replacement

Cites Work

• Unknotting number one knots are prime
• Splitting the PL involutions of nonprime 3-manifolds
• Unknotting number, genus and companion tori
• Only integral Dehn surgeries can yield reducible manifolds

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