Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Kawauchi conjecture about the Conway polynomial of achiral knots   We give a counterexample to the Kawauchi conjecture on the Conway polynomial
of achiral knots which asserts that the Conway polynomial $C(z)$ of an achiral
knot satisfies the splitting property $C(z)=F(z)F(-z)$ for a polynomial $F(z)$
with integer coefficients. We show that the Bonahon-Siebenmann decomposition of
an achiral and alternating knot is reflected in the Conway polynomial. More
explicitly, the Kawauchi conjecture is true for quasi-arborescent knots and
counterexamples in the class of alternating knots must be quasi-polyhedral.

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The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con