Tunnel number one knots, 𝑚-small knots and the Morimoto conjecture

DOI10.1090/S0002-9939-2013-11700-4zbMath1282.57015WikidataQ123367162 ScholiaQ123367162MaRDI QIDQ2855919

Xunbo Yin, Guo-Qiu Yang, Feng Chun Lei

Publication date: 23 October 2013

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

zbMATH Keywords

tunnel number\(m\)--smallMorimoto conjecture

Mathematics Subject Classification ID

Cites Work

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• Heegaard genus of the connected sum of \(m\)-small knots
• Knot exteriors with additive Heegaard genus and Morimoto's conjecture
• Knots with \(g(E(K))=2\) and \(g(E(K\#K\#K))=6\) and Morimoto's conjecture
• Reducing Heegaard splittings
• The tunnel number of the sum of \(n\) knots is at least \(n\)
• Closed incompressible surfaces in complements of wide knots and links
• Local detection of strongly irreducible Heegaard splittings
• On the additivity of tunnel number of knots
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• Heegaard structures of negatively curved 3-manifolds
• On the super additivity of tunnel number of knots
• Additivity of tunnel number for small knots
• Tunnel number, connected sum and meridional essential surfaces
• The Classification of Heegaard Splittings for (Compact Orient Able Surface) × S¹
• A CONSTRUCTION OF ARBITRARILY HIGH DEGENERATION OF TUNNEL NUMBERS OF KNOTS UNDER CONNECTED SUM
• Tunnel numbers of small knots do not go down under connected sum
• There are Knots whose Tunnel Numbers go down under Connected Sum
• Examples of tunnel number one knots which have the property ‘1 + 1 = 3’

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