Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Parities and Coverings over Free Knots   In the present paper, we develop the parity theory invented in \cite{ManSb};
we construct new parities for two-component (virtual and free) links. New
parities significantly depend on geometrical properties of diagrams; in
particular, they are mutation-sensitive.
  New parities can be used practically in all problems, where parities were
previously applied.

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The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con