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dc.contributor.author조상범-
dc.date.accessioned2018-04-14T04:37:10Z-
dc.date.available2018-04-14T04:37:10Z-
dc.date.issued2011-01-
dc.identifier.citationAmerican Mathematical Society, 2011, 361(1), P.259-280en_US
dc.identifier.issn0002-9947-
dc.identifier.urihttp://www.ams.org/journals/tran/2011-363-01/S0002-9947-2010-05248-1/home.html-
dc.description.abstractWe use the theory of tunnel number 1 knots introduced in an earlier paper to strengthen the Tunnel Leveling Theorem of Goda, Scharlemann, and Thompson. This yields considerable information about bridge numbers of tunnel number 1 knots. In particular, we calculate the minimum bridge number of a knot as a function of the maximum depth invariant d of its tunnels. The growth of this value is on the order of (1 + root 2)(d), which improves known estimates of the rate of growth of bridge number as a function of the Hempel distance of the associated Heegaard splitting. We also find the maximum bridge number as a function of the number of cabling constructions needed to produce the tunnel, showing in particular that the maximum bridge number of a knot produced by n cabling constructions is the (n + 2)(nd) Fibonacci number. Finally, we examine the special case of the "middle" tunnels of torus knots.en_US
dc.description.sponsorshipThe second author was supported in part by NSF grant DMS-0802424.en_US
dc.language.isoenen_US
dc.publisherAmerican Mathematical SOCen_US
dc.subjectUNKNOTTING TUNNELSen_US
dc.subjectHEEGAARDen_US
dc.subject3-SPHEREen_US
dc.subjectPRESERVEen_US
dc.subjectKNOTSen_US
dc.subjectDECOMPOSITIONSen_US
dc.subjectAUTOMORPHISMSen_US
dc.subjectDISTANCEen_US
dc.subjectGENUS-2en_US
dc.subjectSPACESen_US
dc.titleTUNNEL LEVELING, DEPTH, AND BRIDGE NUMBERSen_US
dc.typeArticleen_US
dc.relation.no1-
dc.relation.volume363-
dc.identifier.doi10.1090/S0002-9947-2010-05248-1-
dc.relation.page259-280-
dc.relation.journalTRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY-
dc.relation.code2011209536-
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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