Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Volume of representations and mapping degree   Given a connected real Lie group and a contractible homogeneous proper
$G$--space $X$ furnished with a $G$--invariant volume form, a real valued
volume can be assigned to any representation $\rho\colon \pi_1(M)\to G$ for any
oriented closed smooth manifold $M$ of the same dimension as $X$. Suppose that
$G$ contains a closed and cocompact semisimple subgroup, it is shown in this
paper that the set of volumes is finite for any given $M$. From a perspective
of model geometries, examples are investigated and applications with mapping
degrees are discussed.

36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph