Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 non-concordant 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-concordant knots having the same Seifert form as the knot. As a
corollary, no nontrivial Alexander polynomial determines a unique knot
concordance class. We use Cochran-Orr-Teichner's recent result on the knot
concordance group and Cheeger-Gromov's von Neumann rho invariants with their
universal bound for a 3-manifold.

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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat