Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transverse foliations on the torus $\T^2$ and partially hyperbolic
  diffeomorphisms on 3-manifolds   In this paper, we prove that given two $C^1$ foliations $\mathcal{F}$ and
$\mathcal{G}$ on $\mathbb{T}^2$ which are transverse, there exists a non-null
homotopic loop $\{\Phi_t\}_{t\in[0,1]}$ in $\diff^{1}(\T^2)$ such that
$\Phi_t(\calF)\pitchfork \calG$ for every $t\in[0,1]$, and $\Phi_0=\Phi_1= Id$.
As a direct consequence, we get a general process for building new partially
hyperbolic diffeomorphisms on closed $3$-manifolds. \cite{BPP} built a new
example of dynamically coherent non-transitive partially hyperbolic
diffeomorphism on a closed $3$-manifold, the example in \cite{BPP} is obtained
by composing the time $t$ map, $t>0$ large enough, of a very specific
non-transitive Anosov flow by a Dehn twist along a transverse torus. Our result
shows that the same construction holds starting with any non-transitive Anosov
flow on an oriented $3$-manifold. Moreover, for a given transverse torus, our
result explains which type of Dehn twists lead to partially hyperbolic
diffeomorphisms.

6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess