Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing theorems on covering manifolds   Let $M$ be an oriented even-dimensional Riemannian manifold on which a
discrete group $\Gamma$ of orientation-preserving isometries acts freely, so
that the quotient $X=M/\Gamma$ is compact. We prove a vanishing theorem for a
half-kernel of a $\Gamma$-invariant Dirac operator on a $\Gamma$-equivariant
Clifford module over $M$, twisted by a sufficiently large power of a
$\Gamma$-equivariant line bundle, whose curvature is non-degenerate at any
point of $M$. This generalizes our previous vanishing theorems for Dirac
operators on a compact manifold.
  In particular, if $M$ is an almost complex manifold we prove a vanishing
theorem for the half-kernel of a $\spin^c$ Dirac operator, twisted by a line
bundle with curvature of a mixed sign. In this case we also relax the
assumption of non-degeneracy of the curvature. When $M$ is a complex manifold
our results imply analogues of Kodaira and Andreotti-Grauert vanishing theorems
for covering manifolds.
  As another application, we show that semiclassically the $\spin^c$
quantization of an almost complex covering manifold gives an "honest" Hilbert
space. This generalizes a result of Borthwick and Uribe, who considered
quantization of compact manifolds.
  Application of our results to homogeneous manifolds of a real semisimple Lie
group leads to new proofs of Griffiths-Schmidt and Atiyah-Schmidt vanishing
theorems.

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The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
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The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th