Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete affine manifolds with Anosov holonomy groups II: partially
  hyperbolic holonomy and cohomological dimensions   Let $N$ be a complete affine manifold $A^n/\Gamma$ of dimension $n$ where
$\Gamma$ is an affine transformation group and $K(\Gamma, 1)$ is realized as a
finite CW-complex. $N$ has a partially hyperbolic holonomy group if the tangent
bundle pulled over the unit tangent bundle over a sufficiently large compact
part splits into expanding, neutral, and contracting subbundles along the
geodesic flow. We show that if the holonomy group is partially hyperbolic of
index $k$, $k < n/2$, then $\mathrm{cd}(\Gamma) \leq n-k$. Moreover, if a
finitely-presented affine group $\Gamma$ acts on $A^n$ properly discontinuously
and freely with the $k$-Anosov linear group for $k \leq n/2$, then
$\mathrm{cd}(\Gamma) \leq n-k$. Also, there exists a compact collection of
$n-k$-dimensional affine subspaces where $\Gamma$ acts on. The techniques here
are mostly from coarse geometry.

23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess