Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double branched covers of theta-curves   We prove a folklore theorem of W. Thurston which provides necessary and
sufficient conditions for primality of a certain class of theta-curves. Namely,
a theta-curve in the 3-sphere with an unknotted constituent knot U is prime if
and only if lifting the third arc of the theta-curve to the double branched
cover over U produces a prime knot. We apply this result to Kinoshita's
theta-curve.

13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org