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...
متن کاملStable Concordance of Knots in 3–manifolds
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 ...
متن کاملKnot Mutation: 4–genus of Knots and Algebraic Concordance
Kearton observed that mutation can change the concordance class of a knot. A close examination of his example reveals that it is of 4–genus 1 and has a mutant of 4–genus 0. The first goal of this paper is to construct examples to show that for any pair of nonnegative integers m and n there is a knot of 4–genus m with a mutant of 4–genus n. A second result of this paper is a crossing change form...
متن کاملRibbon Concordance of Surface-knots via Quandle Cocycle Invariants
We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the invariant already known. We demonstrate that twist-spins of some torus knots are not ribbon concordant to their orientation reversed images.
متن کاملSplitting the Concordance Group of Algebraically Slice Knots
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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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 1983
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004100060801