A Partial Order of Knots
نویسندگان
چکیده
منابع مشابه
A Graph-Theoretic Approach to a Partial Order of Knots and Links
We say that a link L1 is an s-major of a link L2 if any diagram of L1 can be transformed into a diagram of L2 by changing some crossings and smoothing some crossings. This relation is a partial ordering on the set of all prime alternating links. We determine this partial order for all prime alternating knots and links with the crossing number less than or equal to six. The proofs are given by g...
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In 1977 Gordon [G] asked whether every class of order two in the classical knot concordance group can be represented by an amphicheiral knot. The question remains open although counterexamples in higher dimensions are now known to exist [CM]. This problem is more naturally stated in terms of negative amphicheiral knots, since such knots represent 2–torsion in concordance; that is, if K is negat...
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The twisted Alexander polynomial was introduced by Lin [9] and Wada [18] independently. Lin defined it for a knot by using a regular Seifert surface and Wada defined it for a finitely presentable group by using Fox’s free differential calculus. More generally, Jiang and Wang [3] studied twisted topological invariants for a 3–manifold by using representations of the fundamental group. Following ...
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For certain classes of knots we define geometric invariants called higher-order genera. Each of these invariants is a refinement of the slice genus of a knot. We find lower bounds for the higherorder genera in terms of certain von Neumann ρ-invariants, which we call higher-order signatures. The higher-order genera offer a refinement of the Grope filtration of the knot concordance group.
متن کاملOrder 2 Algebraically Slice Knots
The concordance group of algebraically slice knots is the subgroup of the classical knot concordance group formed by algebraically slice knots. Results of Casson and Gordon and of Jiang showed that this group contains in infinitely generated free (abelian) subgroup. Here it is shown that the concordance group of algebraically slice knots also contain elements of finite order; in fact it contain...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 1989
ISSN: 0387-3870
DOI: 10.3836/tjm/1270133558