Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Linking Number Definition of the Affine Index Polynomial and
  Applications   This paper gives an alternate definition of the Affine Index Polynomial
(called the Wriggle Polynomial) using virtual linking numbers and explores
applications of this polynomial. In particular, it proves the Cosmetic Crossing
Change Conjecture for odd virtual knots and pure virtual knots. It also
demonstrates that the polynomial can detect mutations by positive rotation and
proves it cannot detect mutations by positive reflection. Finally it exhibits a
pair of mutant knots that can be distinguished by a Type 2 Vassiliev Invariant
coming from the polynomial.

21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
1
The categories of this paper are: cs
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The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics