Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic aspects of polar actions   An isometric compact group action $G \times (M,g) \rightarrow (M,g)$ is
called polar if there exists a closed embedded submanifold $\Sigma \subseteq M$
which meets all orbits orthogonally. Let $\Pi$ be the associated generalized
Weyl group. We study the properties of the lifting action $G$ on the cotangent
bundle $T^*M$. In particular, we show that the restriction map
$(C^{\infty}(T^*M))^G \rightarrow (C^{\infty}(T^* \Sigma))^{\Pi}$ is a
surjective homomorphism of Poisson algebras. As a corollary, the singular
symplectic reductions $T^*M // G $ and $T^* \Sigma // \Pi$ are isomorphic as
stratified symplectic spaces, which gives a partial answer to a conjecture of
Lerman, Montgomery and Sjamaar.

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The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph