Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global rigidity of actions by higher rank lattices with dominated
  splitting   We prove that any smooth volume-preserving action of a lattice $\Gamma$ in
$\textrm{SL}(n,\mathbb{R})$, $n\ge 3$, on a closed $n$-manifold which possesses
one element that admits a dominated splitting should be standard. In other
words, the manifold is the $n$-flat torus and the action is smoothly conjugate
to an affine action. Note that an Anosov diffeomorphism, or more generally, a
partial hyperbolic diffeomorphism admits a dominated splitting. We have a
topological global rigidity when $\alpha$ is $C^{1}$. Similar theorems hold for
an action of a lattice in $\textrm{Sp}(2n,\mathbb{R})$ with $n\ge 2$ and
$\textrm{SO}(n,n)$ with $n\ge 5$ on a closed $2n$-manifold.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph