Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orderability of link quandles   The paper develops a general theory of orderability of quandles with a focus
on link quandles of tame links and gives some general constructions of
orderable quandles. We prove that knot quandles of many fibered prime knots are
right-orderable, whereas link quandles of most non-trivial torus links are not
right-orderable. As a consequence, we deduce that the knot quandle of the
trefoil is neither left nor right orderable. Further, it is proved that link
quandles of certain non-trivial positive (or negative) links are not
bi-orderable, which includes some alternating knots of prime determinant and
alternating Montesinos links. The paper also explores interconnections between
orderability of quandles and that of their enveloping groups. The results
establish that orderability of link quandles behave quite differently than that
of corresponding link groups.

11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat