Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pullbacks of metric bundles and Cannon-Thurston maps   We introduce the notion of pullbacks of metric bundles. Given a metric
(graph) bundle $X$ over $B$ where $X$ and all the fibers are uniformly (Gromov)
hyperbolic and nonelementary, and a Lipschitz qi embedding $i: A\rightarrow B$
we show that the pullback $i^{*}X$ is hyperbolic and the map $i^{*}:
i^{*}X\rightarrow X$ admits a continuous boundary extension, i.e. a
Cannon-Thurston (CT) map $\partial i^{*}:\partial( i^{*}X) \rightarrow \partial
X$. As an application of our theorem we show that given a short exact sequence
of nonelementary hyperbolic groups $1\rightarrow N\rightarrow
G\stackrel{\pi}{\rightarrow} Q\rightarrow 1$ and a finitely generated qi
embedded subgroup $Q_1<Q$, $G_1:=\pi^{-1}(Q_1)$ is hyperbolic and the inclusion
$G_1\rightarrow G$ admits a CT map $\partial G_1\rightarrow \partial G$.

35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom