TUNNEL LEVELING, DEPTH, AND BRIDGE NUMBERS
DC Field | Value | Language |
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dc.contributor.author | Cho, Sang bum | - |
dc.contributor.author | McCullough, Darryl | - |
dc.date.accessioned | 2022-07-16T22:11:44Z | - |
dc.date.available | 2022-07-16T22:11:44Z | - |
dc.date.created | 2021-05-13 | - |
dc.date.issued | 2011-01 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/169176 | - |
dc.description.abstract | We 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. | - |
dc.language | 영어 | - |
dc.language.iso | en | - |
dc.publisher | AMER MATHEMATICAL SOC | - |
dc.title | TUNNEL LEVELING, DEPTH, AND BRIDGE NUMBERS | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Cho, Sang bum | - |
dc.identifier.doi | 10.1090/S0002-9947-2010-05248-1 | - |
dc.identifier.scopusid | 2-s2.0-78651296805 | - |
dc.identifier.wosid | 000282653700013 | - |
dc.identifier.bibliographicCitation | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.363, no.1, pp.259 - 280 | - |
dc.relation.isPartOf | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.citation.title | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | - |
dc.citation.volume | 363 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 259 | - |
dc.citation.endPage | 280 | - |
dc.type.rims | ART | - |
dc.type.docType | 정기학술지(Article(Perspective Article포함)) | - |
dc.description.journalClass | 1 | - |
dc.description.isOpenAccess | Y | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
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