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Showing 1 to 4 of 4 for “"Knot concordance"”.
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Witt Rings and Algebraic Knot Concordance
The (knot) concordance group was introduced by Fox and Milnor in 1966. Since then some progress has been made studying both slice knots and concordance, though even some basic questions remain unanswered. We discuss the construction of the concordance group starting from knotted circles in S^3. Of …
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First Order Signatures and Knot Concordance
Invariants of knots coming from twisted signatures have played a central role in the study of knot concordance. Unfortunately, except in the simplest of cases, these signature invariants have proven exceedingly difficult to compute. As a consequence, many knots which presumably can be detected by …
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Casson towers and filtrations of the smooth knot concordance group
The 4-dimensional equivalence relation of concordance (smooth or topological) gives a group structure on the set of knots, under the connected-sum operation. The n-solvable filtration of the knot concordance group (denoted C), due to Cochran-Orr-Teichner, has been instrumental in the study of knot …
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Shake Slice and Shake Concordant Links
The study of knots and links up to concordance has proved significant for many problems in low dimensional topology. In the 1970s, Akbulut introduced the notion of shake concordance of knots, a generalization of the study of knot concordance. Recent work of Cochran and Ray has advanced our …