Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Determining the Topology of the Observable Universe via 3-D Quasar
  Positions   Hot big bang cosmology says nothing about the topology of the Universe. A
topology-independent algorithm is presented which is complementary to that of
Lehoucq et al. 1996 and which searches for evidence of multi-connectedness
using catalogues of astrophysically observed objects. The basis of this
algorithm is simply to search for a quintuplet of quasars (over a region of a
few hundred comoving Mpc) which can be seen in two different parts of our past
time cone, allowing for a translation, an arbitrary rotation and possibly a
reflection. This algorithm is demonstrated by application to the distribution
of quasars between redshifts of $z=1$ and $z\approx4,$ i.e., at a comoving
distance from the observer $1700 h^{-1}\mbox{\rm Mpc} \ltapprox d \ltapprox
3300 h^{-1}\mbox{\rm Mpc}.$ Two pairs of isometric quintuplets separated by
more than {$300$\hMpc} are found. This is consistent with the number expected
from Monte Carlo simulations in a simply connected Universe if the detailed
anisotropy of sky coverage by the individual quasar surveys is taken into
account. The linear transformation in (flat) comoving space from one quintuplet
to another requires translations of {$353$\hMpc} and {4922\hMpc} respectively,
plus a reflection in the former case, and plus both a rotation and a reflection
in the latter. Since reflections are required, if these two matches were due to
multi-connectedness, then the Universe would be non-orientable.

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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
31
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: patt-sol
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The categories of this paper are: dg-ga
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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: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: physics
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The categories of this paper are: atom-ph