Parameterizations of 1-bridge torus knots

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dc.contributor.authorChoi, DHko
dc.contributor.authorKo, Ki-Hyoungko
dc.date.accessioned2013-03-04T17:52:28Z-
dc.date.available2013-03-04T17:52:28Z-
dc.date.created2012-02-06-
dc.date.created2012-02-06-
dc.date.issued2003-06-
dc.identifier.citationJOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v.12, no.4, pp.463 - 491-
dc.identifier.issn0218-2165-
dc.identifier.urihttp://hdl.handle.net/10203/83520-
dc.description.abstractA 1-bridge torus knot in a 3-manifold of genus less than or equal to 1 is a knot drawn on a Heegaard torus with one bridge. We give two types of normal forms to parameterize the family of 1-bridge torus knots that are similar to the Schubert's normal form and the Conway's normal form for 2-bridge knots. For a given Schubert's normal form we give algorithms to determine the number of components and to compute the fundamental group of the complement when the normal form determines a knot. We also give a description of the double branched cover of an ambient 3-manifold branched along a 1-bridge torus knot by using its Conway's normal form and obtain an explicit formula for the first homology of the double cover.-
dc.languageEnglish-
dc.publisherWORLD SCIENTIFIC PUBL CO PTE LTD-
dc.subjectNUMBER ONE KNOTS-
dc.subjectBRAID GROUPS-
dc.titleParameterizations of 1-bridge torus knots-
dc.typeArticle-
dc.identifier.wosid000184173600003-
dc.identifier.scopusid2-s2.0-0042031148-
dc.type.rimsART-
dc.citation.volume12-
dc.citation.issue4-
dc.citation.beginningpage463-
dc.citation.endingpage491-
dc.citation.publicationnameJOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS-
dc.contributor.localauthorKo, Ki-Hyoung-
dc.contributor.nonIdAuthorChoi, DH-
dc.type.journalArticleArticle-
dc.subject.keywordAuthor1-bridge torus knot-
dc.subject.keywordAuthor(1,1)-knot-
dc.subject.keywordAuthorparameterization-
dc.subject.keywordAuthornormal form-
dc.subject.keywordAuthordouble branched cover-
dc.subject.keywordPlusNUMBER ONE KNOTS-
dc.subject.keywordPlusBRAID GROUPS-
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