hi cosmic topologists,
Today we have *two* cosmic topology articles on arXiv on the same day!
(1) http://arxiv.org/abs/1009.5880 Cosmic microwave anisotropies in an inhomogeneous compact flat universe Authors: R. Aurich, S. Lustig
This shows that the half-turn space E_2 also seems to provide a nice fit, at least with the S_60deg statistic, to the WMAP 7yr data, and it even seems to be a bit better than T^3.
(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 ?
cheers boud
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
hi cos-top!
Zitat von Boud Roukema boud@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
Cos-top mailing list Cos-top@cosmo.torun.pl http://cosmo.torun.pl/mailman/listinfo/cos-top
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
hi Sven, cos-top,
On Thu, 10 May 2012, sven.lustig uni-ulm.de wrote:
Zitat von Boud Roukema <boud astro.uni.torun.pl>:
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.
Thanks for the correction - I think you are saying that these are orbifolds that are not manifolds. Is that right?
From what I understand (e.g. [1] and discussions with Jeff and Vincent),
manifold without boundary \Rightarrow orbifold, but orbifold \not\Rightarrow manifold.
So that means that the word descriptions of N8-N10 in http://arxiv.org/abs/1009.5825 (v1 and published version) are incorrect in the sense that these are not 3-manifolds, although they are 3-orbifolds.
Also, do you mean N8-N10? I don't see N11 defined in 1009.5285.
cheers boud
hi Boud, cos-top,
yes! N8-N10 that are orbifolds.
In arXiv:1201.1875 N8-N10 are also called orbifolds. In this paper one finds the orbifold N11.
Best, Sven
Zitat von Boud Roukema boud@astro.uni.torun.pl:
hi Sven, cos-top,
On Thu, 10 May 2012, sven.lustig uni-ulm.de wrote:
Zitat von Boud Roukema <boud astro.uni.torun.pl>:
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.
Thanks for the correction - I think you are saying that these are orbifolds that are not manifolds. Is that right?
From what I understand (e.g. [1] and discussions with Jeff and Vincent), manifold without boundary \Rightarrow orbifold, but orbifold \not\Rightarrow manifold.
So that means that the word descriptions of N8-N10 in http://arxiv.org/abs/1009.5825 (v1 and published version) are incorrect in the sense that these are not 3-manifolds, although they are 3-orbifolds.
Also, do you mean N8-N10? I don't see N11 defined in 1009.5285.
cheers boud
[1] http://en.wikipedia.org/wiki/Orbifold
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