Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Centralizers of Hamiltonian circle actions on rational ruled surfaces   In this paper, we compute the homotopy type of the group of equivariant
symplectomorphisms of $S^2 \times S^2$ and $\mathbb{C}P^2 \#
\overline{\mathbb{C}P^2}$ under the presence of Hamiltonian group actions of
the circle $S^1$. We prove that the group of equivariant symplectomorphisms are
homotopy equivalent to either a torus, or to the homotopy pushout of two tori
depending on whether the circle action extends to a single toric action or to
exactly two non-equivalent toric actions. This follows from the analysis of the
action of equivariant symplectomorphisms on the space of compatible and
invariant almost complex structures $\mathcal{J}^{S^1}_{\omega}$. In
particular, we show that this action preserves a decomposition of
$\mathcal{J}^{S^1}_{\omega}$ into strata which are in bijection with toric
extensions of the circle action. Our results rely on $J$-holomorphic
techniques, on Delzant's classification of toric actions and on Karshon's
classification of Hamiltonian circle actions on $4$-manifolds.

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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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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: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph