[Cos-top] half-turn space analysis; new spherical 3-manifolds ?

[Boud Roukema]

hi cos-top

On Thu, 30 Sep 2010, Boud Roukema wrote:

> (2) http://arxiv.org/abs/1009.5825
> Multipole analysis in cosmic topology
> Authors: Peter Kramer
>
> This seems to claim that the author has found 3 new spherical
> 3-manifolds, "N8, N9, N10". It's not clear to me if he claims that
> they can be given constant curvature, but maybe it's obvious to
> someone who knows the mathematics a bit better.  i had thought that
> the constant curvature spherical 3-manifolds were already completely
> classified.
>
> Are N8, N9, and N10 new constant-curvature spherical 3-manifolds, in
> addition to those in Gausmann et al. 2001 http://arxiv.org/abs/gr-qc/0106033 
> ?

It looks like I forgot to reply on-list. From off-list discussion, it's
clear that these are just specific examples of constant curvature
spherical 3-manifolds. They are claimed to be "new" in the sense of not
having been specifically described in this way before, without claiming
that they are additional to the standard classification.

Aurich, Kramer & Lustig [1] give a direct answer in terms of the
similarly defined N2 and N3:

   N2 is a construction of the lens space L(8,3) - which is globally
   inhomogeneous - by starting at a specifically chosen point, around
   which the Dirichlet/Voronoi domain happens to be ... a cube;

and

   N3 = S^3/D_8^*.

cheers
boud


[1] Aurich, Kramer & Lustig, 2011,  Physica Scripta 84, 055901, arXiv:1107.5214