Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolic rank and subexponential corank of metric spaces   We introduce a new quasi-isometry invariant $\subcorank X$ of a metric space
$X$ called {\it subexponential corank}. A metric space $X$ has subexponential
corank $k$ if roughly speaking there exists a continuous map $g:X\to T$ such
that for each $t\in T$ the set $g^{-1}(t)$ has subexponential growth rate in
$X$ and the topological dimension $\dim T=k$ is minimal among all such maps.
Our main result is the inequality $\hyprank X\le\subcorank X$ for a large class
of metric spaces $X$ including all locally compact Hadamard spaces, where
$\hyprank X$ is maximal topological dimension of $\di Y$ among all $\CAT(-1)$
spaces $Y$ quasi-isometrically embedded into $X$ (the notion introduced by M.
Gromov in a slightly stronger form). This proves several properties of
$\hyprank$ conjectured by M. Gromov, in particular, that any Riemannian
symmetric space $X$ of noncompact type possesses no quasi-isometric embedding
$\hyp^n\to X$ of the standard hyperbolic space $\hyp^n$ with $n-1>\dim X-\rank
X$.

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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys