Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symplectic quotients and representability: the circle action case   Let $S^1$ act on a symplectic manifold in a Hamiltonian fashion with momentum
map $\Psi$. Fix a value $a$ of $\Psi$. There is a question of whether the
symplectic quotient at $a$ is diffeomorphic to the orbit space of some proper
Lie group action. We prove under mild assumptions that this only occurs if the
symplectic quotient is diffeomorphic to an effective orbifold. This, in turn,
only occurs if $a$ is a regular value, or there is at most one positive weight
or at most one negative weight.

30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys