Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intersection cohomology of rank two character varieties of surface
  groups   For $G = \mathrm{GL}_2, \mathrm{SL}_2, \mathrm{PGL}_2$ we compute the
intersection E-polynomials and the intersection Poincar\'e polynomials of the
$G$-character variety of a compact Riemann surface $C$ and of the moduli space
of $G$-Higgs bundles on $C$ of degree zero. We derive several results
concerning the P=W conjectures for these singular moduli spaces.

3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th