Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology of Moduli Spaces of Free Group Representations in Real
  Reductive Groups   Let $G$ be a real reductive algebraic group with maximal compact subgroup
$K$, and let $F_r$ be a rank $r$ free group. We show that the space of closed
orbits in $\mathrm{Hom}(F_r,G)/G$ admits a strong deformation retraction to the
orbit space $\mathrm{Hom}(F_r,K)/K$. In particular, all such spaces have the
same homotopy type. We compute the Poincar\'e polynomials of these spaces for
some low rank groups $G$, such as $\mathrm{Sp}(4,\mathbb{R})$ and
$\mathrm{U}(2,2)$. We also compare these real moduli spaces to the real points
of the corresponding complex moduli spaces, and describe the geometry of many
examples.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess