Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The exponential law for spaces of test functions and diffeomorphism
  groups   We prove the exponential law $\mathcal A(E \times F, G) \cong \mathcal
A(E,\mathcal A(F,G))$ (bornological isomorphism) for the following classes
$\mathcal A$ of test functions: $\mathcal B$ (globally bounded derivatives),
$W^{\infty,p}$ (globally $p$-integrable derivatives), $\mathcal S$ (Schwartz
space), $\mathcal D$ (compact sport, $\mathcal B^{[M]}$ (globally
Denjoy_Carleman), $W^{[M],p}$ (Sobolev_Denjoy_Carleman), $\mathcal
S_{[L]}^{[M]}$ (Gelfand_Shilov), and $\mathcal D^{[M]}$. Here $E, F, G$ are
convenient vector spaces (finite dimensional in the cases of $W^{\infty,p}$,
$\mathcal D$, $W^{[M],p}$, and $\mathcal D^{[M]})$, and $M=(M_k)$ is a weakly
log-convex weight sequence of moderate growth. As application we give a new
simple proof of the fact that the groups of diffeomorphisms
$\operatorname{Diff} \mathcal B$, $\operatorname{Diff} W^{\infty,p}$,
$\operatorname{Diff} \mathcal S$, and $\operatorname{Diff}\mathcal D$ are
$C^\infty$ Lie groups, and $\operatorname{Diff} \mathcal B^{\{M\}}$,
$\operatorname{Diff}W^{\{M\},p}$, $\operatorname{Diff} \mathcal
S_{\{L\}}^{\{M\}}$, and $\operatorname{Diff}\mathcal D^{[M]}$, for
non-quasianalytic $M$, are $C^{\{M\}}$ Lie groups, where
$\operatorname{Diff}\mathcal A = \{\operatorname{Id} +f : f \in \mathcal
A(\mathbb R^n,\mathbb R^n), \inf_{x \in \mathbb R^n} \det(\mathbb I_n+
df(x))>0\}$. We also discuss stability under composition.

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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th