Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sections of Lie group actions and a theorem by M. Newman   Let $M$ be a smooth finite-dimensional manifold, $G$ be a Lie group, and
$\Phi:G \times M \to M$ be a smooth action. Consider the following mapping
$\phi: C^{\infty}(M,G) \to C^{\infty}(M,M)$, defined by $\phi(\alpha)(x) =
\alpha(x)\cdot x$, for $\alpha\in C^{\infty}(M,G)$ and $x\in M$. In this paper
we describe the structure of inverse images of elements of $C^{\infty}(M,M)$
under $\phi$ for $\dim G=1$, i.e. when $G$ is either $\mathbb{R}$ or $S^1$. As
an application we obtain a new proof of the well-known theorem by M. Newman
concerning the interior of the fixed point set of a Lie group action.

14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn