Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An asymptotic dimension for metric spaces, and the 0-th Novikov-Shubin
  invariant   A nonnegative number d_infinity, called asymptotic dimension, is associated
with any metric space. Such number detects the asymptotic properties of the
space (being zero on bounded metric spaces), fulfills the properties of a
dimension, and is invariant under rough isometries. It is then shown that for a
class of open manifolds with bounded geometry the asymptotic dimension
coincides with the 0-th Novikov-Shubin number alpha_0 defined previously
(math.OA/9802015, cf. also math.DG/0110294). Thus the dimensional
interpretation of alpha_0 given in the mentioned paper in the framework of
noncommutative geometry is established on metrics grounds. Since the asymptotic
dimension of a covering manifold coincides with the polynomial growth of its
covering group, the stated equality generalises to open manifolds a result by
Varopoulos.

6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
1
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: gr-qc
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The categories of this paper are: hep-lat