On tunnel number degeneration and 2-string free tangle decompositions

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dc.contributor.advisorGordon, Cameron, 1945-en
dc.contributor.committeeMemberBajaj, Chandraen
dc.contributor.committeeMemberGompf, Roberten
dc.contributor.committeeMemberLuecke, Johnen
dc.contributor.committeeMemberMarcotte, Edwarden
dc.contributor.committeeMemberReid, Alanen
dc.creatorNogueira, João Miguel Dias Ferreiraen
dc.date.accessioned2012-02-21T20:59:40Zen
dc.date.accessioned2017-05-11T22:24:38Z
dc.date.available2012-02-21T20:59:40Zen
dc.date.available2017-05-11T22:24:38Z
dc.date.issued2011-12en
dc.date.submittedDecember 2011en
dc.date.updated2012-02-21T20:59:53Zen
dc.descriptiontexten
dc.description.abstractThis dissertation is on a study of 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't degenerate by more than one: t(K_1#K_2)≥ t(K_1)+t(K_2)-1, for K_1 and K_2 prime knots. We also study 2-string free tangle decompositions of links with tunnel number two and obtain an equivalent statement to the one on knots. Further observations on tunnel number and essential tangle decompositions are also made.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.slug2152/ETD-UT-2011-12-4617en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2011-12-4617en
dc.language.isoengen
dc.subjectTunnel numberen
dc.subjectDegeneration ratioen
dc.subjectPrime knotsen
dc.subject2-string free tangle decompositionsen
dc.titleOn tunnel number degeneration and 2-string free tangle decompositionsen
dc.type.genrethesisen

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