Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hausdorff Convergence and Universal Covers   We prove that if $Y$ is the Gromov-Hausdorff limit of a sequence of compact
manifolds, $M^n_i$, with a uniform lower bound on Ricci curvature and a uniform
upper bound on diameter, then $Y$ has a universal cover. We then show that, for
$i$ sufficiently large, the fundamental group of $M_i$ has a surjective
homeomorphism onto the group of deck transforms of $Y$. Finally, in the
non-collapsed case where the $M_i$ have an additional uniform lower bound on
volume, we prove that the kernels of these surjective maps are finite with a
uniform bound on their cardinality. A number of theorems are also proven
concerning the limits of covering spaces and their deck transforms when the
$M_i$ are only assumed to be compact length spaces with a uniform upper bound
on diameter.

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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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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: plasm-ph
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The categories of this paper are: atom-ph
10
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: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin