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dc.contributor.author조상범-
dc.date.accessioned2018-03-27T02:09:34Z-
dc.date.available2018-03-27T02:09:34Z-
dc.date.issued2013-04-
dc.identifier.citationJournal of the Mathematical Society of Japan, 2013, 65(2), P.671-686en_US
dc.identifier.issn0025-5645-
dc.identifier.issn1881-1167-
dc.identifier.urihttps://projecteuclid.org/euclid.jmsj/1366896647-
dc.identifier.urihttp://hdl.handle.net/20.500.11754/52896-
dc.description.abstractFor a genus-1 1-bridge knot in S-3, that is, a (1,1)-knot, a middle tunnel is a tunnel that is not an upper or lower tunnel for some (1,1)-position. Most torus knots have a middle tunnel, and non-torus-knot examples were obtained by Goda, Hayashi, and Ishihara. In a previous paper, we generalized their construction and calculated the slope invariants for the resulting examples. We give an iterated version of the construction that produces many more examples, and calculate their slope invariants. If one starts with the trivial knot, the iterated constructions produce all the 2-bridge knots, giving a new calculation of the slope invariants of their tunnels. In the final section we compile a list of the known possibilities for the set of tunnels of a given tunnel number 1 knot.en_US
dc.description.sponsorshipThe first author was supported by the research fund of Hanyang University (HY-2011-N).The second author was supported in part by NSF grant DMS-0802424.en_US
dc.language.isoenen_US
dc.publisherMath SOC Japanen_US
dc.subjectknoten_US
dc.subjecttunnelen_US
dc.subject(1,1)en_US
dc.subjecttorus knoten_US
dc.subjectregularen_US
dc.subjectsplittingen_US
dc.subject2-bridgeen_US
dc.titleIterated splitting and the classification of knot tunnelsen_US
dc.typeArticleen_US
dc.relation.no2-
dc.relation.volume65-
dc.identifier.doi10.2969/jmsj/06520671-
dc.relation.page671-686-
dc.relation.journalJOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN-
dc.contributor.googleauthorCho, Sangbum-
dc.contributor.googleauthorMcCullough, Darryl-
dc.relation.code2013011057-
dc.sector.campusS-
dc.sector.daehakCOLLEGE OF EDUCATION[S]-
dc.sector.departmentDEPARTMENT OF MATHEMATICS EDUCATION-
dc.identifier.pidscho-
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COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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