Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental groups of finite volume, bounded negatively curved
  4-manifolds are not 3-manifold groups   We study noncompact, complete, finite volume, Riemannian 4-manifolds $M$ with
sectional curvature $-1<K<0$. We prove that $\pi_1 M$ cannot be a 3-manifold
group. A classical theorem of Gromov says that $M$ is homeomorphic to the
interior of a compact manifold $\M$ with boundary $\partial\barM$. We show that
for each $\pi_1$-injective boundary component $C$ of $\M$, the map $i_*$
induced by inclusion $i\colon C\rightarrow \M$ has infinite index image
$i_*(\pi_1 C)$ in $\pi_1 \M$. We also prove that $M$ cannot be homotoped to be
contained in $\partial\M$.

11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph