  We investigate anomalies reported in the Cosmic Microwave Background maps
from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite on very large
angular scales and discuss possible interpretations. Three independent
anomalies involve the quadrupole and octopole:
  1. The cosmic quadrupole on its own is anomalous at the 1-in-20 level by
being low (the cut-sky quadrupole measured by the WMAP team is more strikingly
low, apparently due to a coincidence in the orientation of our Galaxy of no
cosmological significance);
  2. The cosmic octopole on its own is anomalous at the 1-in-20 level by being
very planar;
  3. The alignment between the quadrupole and octopole is anomalous at the
1-in-60 level.
  Although the a priori chance of all three occurring is 1 in 24000, the
multitude of alternative anomalies one could have looked for dilutes the
significance of such a posteriori statistics. The simplest small universe model
where the universe has toroidal topology with one small dimension of order half
the horizon scale, in the direction towards Virgo, could explain the three
items above. However, we rule this model out using two topological tests: the
S-statistic and the matched circle test.
