Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\pi_1$ of Hamiltonian $S^1$ manifolds   Let $(M, \omega)$ be a connected, compact symplectic manifold equipped with a
Hamiltonian $S^1$ action.
  We prove that, as fundamental groups of topological spaces,
$\pi_1(M)=\pi_1(\hbox{minimum})=\pi_1(\hbox{maximum})=\pi_1(M_{red})$, where
$M_{red}$ is the symplectic quotient at any value in the image of the moment
map $\phi$.

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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: stat