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 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 کاملThe Stable Concordance Genus
The concordance genus of a knot is the least genus of any knot in its concordance class. Although difficult to compute, it is a useful invariant that highlights the distinction between the three-genus and four-genus. In this paper we define and discuss the stable concordance genus of a knot. The stable concordance genus describes the behavior of the concordance genus under connected sum, and ca...
متن کاملKnots of Genus Two
We classify all knot diagrams of genus two and three, and give applications to positive, alternating and homogeneous knots, including a classification of achiral genus 2 alternating knots, slice or achiral 2-almost positive knots, a proof of the 3and 4-move conjectures, and the calculation of the maximal hyperbolic volume for weak genus two knots. We also study the values of the link polynomial...
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 ...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2004
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2004.4.1