Concordance of knots in S1×S2
نویسندگان
چکیده
منابع مشابه
The Concordance Genus of Knots
In knot concordance three genera arise naturally, g(K), g4(K), and gc(K): these are the classical genus, the 4–ball genus, and the concordance genus, defined to be the minimum genus among all knots concordant to K. Clearly 0 ≤ g4(K) ≤ gc(K) ≤ g(K). Casson and Nakanishi gave examples to show that g4(K) need not equal gc(K). We begin by reviewing and extending their results. For knots representin...
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Knots and links in 3-manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato-Levine invariants, and Milnor’s triple linking numbers. Besides fitting into a general theory of Whitney towers, these invariants provide obstructions to the existence of a singular concordance which can be homotoped ...
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As a corollary of work of Ozsváth and Szabó, it is shown that the classical concordance group of algebraically slice knots has an infinite cyclic summand and in particular is not a divisible group. Let A denote the concordance group of algebraically slice knots, the kernel of Levine’s homomorphism φ : C → G, where C is the classical knot concordance group and G is Levine’s algebraic concordance...
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We study the group of rational concordance classes of codimension two knots in rational homology spheres. We give a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, we relate these invariants with limiting behaviour of the Artin reciprocity over an infinite tower of number fields and analyze it using tools from algebraic number theory. In...
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2018
ISSN: 0024-6107
DOI: 10.1112/jlms.12125