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dc.contributor.advisorButler, Leo
dc.contributor.advisorRanicki, Andrew
dc.contributor.authorPowell, Mark Andrew
dc.date.accessioned2011-08-01T12:47:30Z
dc.date.available2011-08-01T12:47:30Z
dc.date.issued2011-06-28
dc.identifier.urihttp://hdl.handle.net/1842/5030
dc.description.abstractLet Knots be the abelian monoid of isotopy classes of knots S1 ⊂ S3 under connected sum, and let C be the topological knot concordance group of knots modulo slice knots. Cochran-Orr-Teichner [COT03] defined a filtration of C: C ⊃ F(0) ⊃ F(0.5) ⊃ F(1) ⊃ F(1.5) ⊃ F(2) ⊃ . . .The quotient C/F(0.5) is isomorphic to Levine’s algebraic concordance group AC1 [Lev69]; F(0.5) is the algebraically slice knots. The quotient C/F(1.5) contains all metabelian concordance obstructions. The Cochran-Orr-Teichner (1.5)-level two stage obstructions map the concordance class of a knot to a pointed set (COT (C/1.5),U). We define an abelian monoid of chain complexes P, with a monoid homomorphism Knots → P. We then define an algebraic concordance equivalence relation on P and therefore a group AC2 := P/ ~, our second order algebraic knot concordance group. The results of this thesis can be summarised in the following diagram: . That is, we define a group homomorphism C → AC2 which factors through C/F(1.5). We can extract the two stage Cochran-Orr-Teichner obstruction theory from AC2: the dotted arrows are morphisms of pointed sets. Our second order algebraic knot concordance group AC2 is a single stage obstruction group.en
dc.contributor.sponsorEngineering and Physical Sciences Research Council (EPSRC)en
dc.language.isoenen
dc.publisherThe University of Edinburghen
dc.subjectabelian monoiden
dc.subjectknotsen
dc.subjectalgebraic concordance groupen
dc.subjectsingle stage obstruction groupen
dc.subjectgeometric topologyen
dc.titleSecond order algebraic knot concordance groupen
dc.typeThesis or Dissertationen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD Doctor of Philosophyen


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