Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Yamabe invariants of orbifolds and cylindrical manifolds, and
  $L^2$-harmonic spinors   We study the Yamabe invariants of cylindrical manifolds and compact orbifolds
with a finite number of singularities, by means of conformal geometry and the
Atiyah-Patodi-Singer $L^2$-index theory. For an $n$-orbifold $M$ with
singularities $\Sigma_{\Gamma} = \{(\check{p}_1, \Gamma_1), ..., (\check{p}_s,
\Gamma_s)\}$ (where each group $\Gamma_j<O(n)$ is of finite order), we define
and study the \emph{orbifold Yamabe invariant} $Y^{\orb}(M)$. We prove that
$Y^{\orb}(M)$ coincides with the corresponding $h$-$\emph{cylindrical Yamabe
invariant}$ $Y^{h\textrm{-}\cyl}(M \setminus \{\check{p}_1, ...,
\check{p}_s\})$ defined by the authors \cite{AB2}, where $h = h_{\Gamma_j}$ is
the standard metric on the slice $S^{n-1}/\Gamma_j$ of each end with infinity
$\check{p}_j$. Using this, we show that $Y^{\orb}(M)$ is bounded by $Y(S^n) /d$
from above, where $d=\max_j|\Gamma_j|^{\frac{2}{n}}$. For a cylindrical
4-manifold $X$ with a general slice metric $h$ on the end, we also establish a
method for estimating the $h$-cylindrical Yamabe invariant
$Y^{h\textrm{-}\cyl}(X)$ from above, in terms of the geometry and topology of
$X$. We conclude by an explicit estimate of $Y^{h\textrm{-}\cyl}(X)$ for
particular cylindrical 4-manifolds $X$, including that of $Y^{\orb}(M)$ for
4-orbifolds $M$.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg