Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An invariant for open virtual strings   Extended Alexander groups are used to define an invariant for open virtual
strings. Examples of non-commuting open strings and a ribbon-concordance
obstruction are given. An example is given of a slice virtual open string that
is not ribbon. Definitions are extended to open n-strings.

36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
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The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph