Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Filamentations and Virtual Knots   In this paper, we discuss filamentations on oriented chord diagrams. When a
filamentation cannot be realized on an oriented chord diagram, then the
corresponding flat virtual knot is non-trivial. If a flat knot diagram is
non-trivial, then any virtual diagram whose shadow is the flat diagram must
also be non-trivial. We introduce a class of flat diagrams for which no
filamentations exist. This class gives the first example of an infinite set of
virtual knots for which the Jones polynomial and the fundamental group both
evaluate trivially. The related generalized Alexander polynomials for the
virtual knots in this class turn out to be distinct, proving that the class is
indeed infinite.

10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th