Only single twists on unknots can produce composite knots

DOI10.1090/S0002-9947-97-01628-0zbMath0883.57005OpenAlexW1548862334MaRDI QIDQ4372608

Chuichiro Hayashi, Kimihiko Motegi

Publication date: 16 December 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-97-01628-0

zbMATH Keywords

knottwistingprimenessScharlemann cycle

Mathematics Subject Classification ID

Related Items (14)

4-Move distance of knots ⋮ Lens spaces and toroidal Dehn fillings ⋮ On composite twisted unknots ⋮ Dehn surgery on knots in solid tori creating essential annuli ⋮ Geometric types of twisted knots ⋮ A SHORT PROOF THAT COMPOSITE TWISTED UNKNOTS ARE SINGLY TWISTED UNKNOTS ⋮ Klein Bottles and Dehn Filling on a Component of Twocomponent Link Exterior ⋮ Obtaining graph knots by twisting unknots ⋮ DEHN FILLINGS CREATING ESSENTIAL SPHERES AND TORI ⋮ Knots and surfaces ⋮ Boundary structure of hyperbolic 3-manifolds admitting toroidal fillings at large distance ⋮ TOROIDAL SURGERIES ON GENUS TWO KNOTS ⋮ Unknotting with a single twist ⋮ On hyperbolic 3-manifolds realizing the maximal distance between toroidal Dehn fillings

Cites Work

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• Unknotting number one knots are prime
• Unknotting number, genus and companion tori
• Reducible manifolds and Dehn surgery
• Unknotting Number One Knots are Prime: A New Proof
• Knots are Determined by Their Complements
• COMPOSITE KNOTS TRIVIALIZED BY TWISTING
• Primeness of Twisted Knots
• On composite twisted unknots
• Twisting Operations and Composite Knot
• Dehn surgery on knots

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