Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Chern numbers and the Hilbert polynomial of an almost complex
  manifold with a circle action   Let $(M,J)$ be a compact, connected, almost complex manifold of dimension
$2n$ endowed with a $J$-preserving circle action with isolated fixed points. In
this note we analyse the `geography problem' for such manifolds, deriving
equations relating the Chern numbers to the index $k_0$ of $(M,J)$. We study
the symmetries and zeros of the Hilbert polynomial associated to $(M,J)$, which
imply many rigidity results for the Chern numbers when $k_0\neq 1$.
  We apply these results to the category of compact, connected symplectic
manifolds. A long-standing question posed by McDuff and Salamon, also known as
the `McDuff conjecture', asked about the existence of non-Hamiltonian actions
with isolated fixed points. This question was answered recently by Tolman, with
an explicit construction of a six-dimensional manifold with such an action. One
issue that this raises is whether one can find topological criteria that ensure
the manifold can only support a Hamiltonian or only a non-Hamiltonian action.
In this vein, we are able to deduce such criteria from our rigidity theorems in
terms of relatively few Chern numbers, depending on the index. This improves
upon results of Feldman for which one needs to know the entire Todd genus.
  Another consequence of our work is that, in the situation above with a
Hamiltonian action, the minimal Chern number coincides with the index and is at
most $n+1$, mirroring results of Michelsohn in the complex category and Hattori
in the almost complex category.

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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas