Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On maximal tori in the contactomorphism groups of regular contact
  manifolds   By a theorem of Banyaga the group of diffeomorphisms of a manifold $P$
preserving a regular contact form $\alpha$ is a central $S^1$ extension of the
commutator of the group of symplectomorphisms of the base $B = P/S^1$. We show
that if $T$ is a Hamiltonian maximal torus in the group of symplectomorphism of
$B$, then its preimage under the extension map is a maximal torus not only in
the group $\Diff(P, \alpha)$ of diffeomorphisms of $P$ preserving $\alpha$ but
also in the much bigger group of contactomorphisms $\Diff (P, \xi)$, the group
of diffeomorphism of $P$ preserving the contact distribution $\xi = \ker
\alpha$. We use this (and the work of Hausmann, and Tolman on polygon spaces)
to give examples of contact manifolds $(P, \xi = \ker \alpha)$ with maximal
tori of different dimensions in their group of contactomorphisms.

37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph