Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elastic Graphs for Main Molecule Matings   Recent work of Dylan Thurston gives a condition for when a post-critically
finite branched self-cover of the sphere is equivalent to a rational map. We
apply D. Thurston's positive criterion for rationality to give a new proof of a
theorem of Rees, Shishikura, and Tan about the mateability of quadratic
polynomials when one polynomial is in the main molecule. These methods may be a
step in understanding the mateability of higher degree post-critically finite
polynomials and demonstrate how to apply the positive criterion to classical
problems.

28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol