Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chern-Simons Theory, Knot Invariants, Vertex Models and Three-manifold
  Invariants   Chern-Simons theories, which are topological quantum field theories, provide
a field theoretic framework for the study of knots and links in three
dimensions. These are rare examples of quantum field theories which can be
exactly and explicitly solved. Expectation values of Wilson link operators
yield a class of link invariants, the simplest of them is the famous Jones
polynomial. Other invariants are more powerful than that of Jones. These new
invariants are sensitive to the chirality of all knots at least upto ten
crossing number unlike those of Jones which are blind to the chirality of some
of them. However, all these invariants are still not good enough to distinguish
a class of knots called mutants. These link invariants can be alternately
obtained from two dimensional vertex models. The $R$-matrix of such a model in
a particular limit of the spectral parameter provides a representation of the
braid group. This in turn is used to construct the link invariants. Exploiting
theorems of Lickorish and Wallace and also those of Kirby, Fenn and Rourke
which relate three-manifolds to surgeries on framed links, these link
invariants in $S^3$ can also be used to construct three-manifold invariants.

24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs