Knots having the same Seifert form and primary decomposition of knot concordance
نویسندگان
چکیده
منابع مشابه
Infinite Family of Non-concordant Knots Having the Same Seifert Form
By a recent result of Livingston, it is known that if a knot has a prime power branched cyclic cover that is not a homology sphere, then there is an infinite family of nonconcordant knots having the same Seifert form as the knot. In this paper, we extend this result to the full extent. We show that if the knot has nontrivial Alexander polynomial, then there exists an infinite family of non-conc...
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For each sequence P = (p1(t), p2(t), . . . ) of polynomials we define a characteristic series of groups, called the derived series localized at P. Given a knot K in S, such a sequence of polynomials arises naturally as the orders of certain submodules of a sequence of higher-order Alexander modules of K. These group series yield filtrations of the knot concordance group that refine the (n)-solv...
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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...
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If a knot K has Seifert matrix VK and has a prime power cyclic branched cover that is not a homology sphere, then there is an infinite family of non–concordant knots having Seifert matrix VK . AMS Classification numbers Primary: 57M25 Secondary: 57N70
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We have a knot quandle and a fundamental class as invariants for a surface-knot. These invariants can be defined for a classical knot in a similar way, and it is known that the pair of them is a complete invariant for classical knots. In this paper, we compare a situation in surface-knot theory with that in classical knot theory, and prove the following: There exist arbitrarily many inequivalen...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2017
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216517501036