Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 3-coloring and other elementary invariants of knots   This paper has two-fold goal: it provides gentle introduction to Knot Theory
starting from 3-coloring, the concept introduced by R. Fox to allow
undergraduate students to see that the trefoil knot is non-trivial, and ending
with statistical mechanics. On the way we prove various (old and new) facts
about knots. We relate Fox 3-colorings to Jones and Kauffman polynomials of
links and we use this connection to sketch the method of approximating the
unknotting number of a knot. We discuss some elementary open problems in knot
theory and show that Fox colorings can be useful in trying to solve them.
Finally we demonstrate how analysis of Fox colorings can lead us to understand
homology and the fundamental group of branched coverings along links.

28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg