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

[sven.lustig at uni-ulm.de]

hi cos-top!

Zitat von Boud Roukema <boud at astro.uni.torun.pl>:

> 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
>
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In the notation of Peter Kramer N1-N7 are platonic manifolds.
In contrast N8-N11 are orbifolds. These orbifolds are generated from  
platonic manifolds using their discret rotation symmetry.

Best
Sven