Structure in the classical knot concordance group
نویسندگان
چکیده
منابع مشابه
Obstructing Four-Torsion in the Classical Knot Concordance Group
In his classification of the knot concordance groups, Levine [L1] defined the algebraic concordance groups, G±, of Witt classes of Seifert matrices and a homomorphism from the odd-dimensional knot concordance groups C4n±1 to G±. The homomorphism is induced by the function that assigns to a knot an associated Seifert matrix: it is an isomorphism on Ck, k ≥ 5; on C3 it is injective, onto an index...
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In 1926 Artin [3] described the construction of knotted 2–spheres in R. The intersection of each of these knots with the standard R ⊂ R is a nontrivial knot in R. Thus a natural problem is to identify which knots can occur as such slices of knotted 2–spheres. Initially it seemed possible that every knot is such a slice knot and it wasn’t until the early 1960s that Murasugi [84] and Fox and Miln...
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Let Knots be the abelian monoid of isotopy classes of knots S ⊂ S under connected sum, and let C be the topological knot concordance group of knots modulo slice knots. Cochran-OrrTeichner [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 kn...
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It is known that if any prime power branched cyclic cover of a knot in S is a homology sphere, then the knot has vanishing Casson-Gordon invariants. We construct infinitely many examples of (topologically) non-slice knots in S whose prime power branched cyclic covers are homology spheres. We show that these knots generate an infinite rank subgroup of F(1.0)/F(1.5) for which Casson-Gordon invari...
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We prove the nontriviality at all levels of the filtration of the classical topological knot concordance group C · · · ⊆ Fn ⊆ · · · ⊆ F1 ⊆ F0 ⊆ C. defined in [COT]. This filtration is significant because not only is it strongly connected to Whitney tower constructions of Casson and Freedman, but all previously-known concordance invariants are related to the first few terms in the filtration. In...
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2004
ISSN: 0010-2571,1420-8946
DOI: 10.1007/s00014-001-0793-6