|WikiProject Mathematics||(Rated Start-class, Low-importance)|
Near the end of the current article, the "link" of a vertex in a triangulated manifold is mentioned, but it is cross-referenced to a different meaning of link (disjoint embeddings of S^1 --> S^3). Is there an article for Thurston's (and others) meaning of the word link? Are the two related (other than that the links of the cusps of a link-complement are the link)? —Preceding unsigned comment added by Lewallen (talk • contribs) 22:02, 10 March 2008 (UTC)
- I fixed the (hyper)link to point to Link (geometry) which is closer to the intended meaning. Even this is not quite adequate, though, as the article Link (geometry) seems to describe the link only in a 2-dimensional simplicial complex. So the article Link (geometry) needs to be fixed. VectorPosse (talk) 22:56, 10 March 2008 (UTC)
Redirection of "Poincare Sphere"
"Poincare sphere" redirects here, however there is another use of the term. In optics, the polarisation state of (fully polarised) light is often described as lying at some position on the "Poincare sphere". In this usage, the Poincare sphere is analogous to a Bloch sphere (especially so for individual photons). Besides the first two results which are Wikipedia, Google seems of the opinion that this is the common usage of the term "Poincare sphere". Perhaps someone (more knowledgeable than I on editing WP) should do something about this. QTachyon 03:03, 25 October 2007 (UTC)
n > 3
The hypothesis that the universe can be described as a Poincare Sphere was, at the time it was suggested in 2003, quite controversial with a number of astronomers saying it had already been disproved. See for example the comments on Prof. Ned Wright's news page at the time:
In particular the following article cited at the above link quotes Spergel, Cornish and Tegmark:
That article suggests the question could be resolved within a few months, and that was six years ago. Should not the Wiki article at least indicate that the claim was contentious and if possible cite some sources addressing the follow-up investigations? There are many discredited speculations in cosmology and some indication should be given if this isn't, as it appears from the page, a mainstream view.
- I asked here: Talk:Planck (spacecraft)#Poincare_sphere There are general questions about topology that seem to linger, see here physics forums. I'm still reading to see what it all says. 220.127.116.11 (talk) 20:12, 6 May 2016 (UTC)
- The final comment on physicsforums seems to wrap it up. I quote in entirety, here:
- I thought Luminet's original idea was very interesting. This link is to one of his papers after WMAP. It seems there are three main predictions: (1) A low value of the quadrupole in the CMB power spectrum. (2) A slightly positive curvature. The best fit in the above paper is ΩK=1.016, and Luminet says in the above paper, " A value lower than 1.01 will discard the Poincare space as a model for cosmic space, in the sense that the size of the corresponding dodecahedron would become greater than the observable universe and would not leave any observable imprint on the CMB, whereas a value greater than 1.01 would strengthen its cosmological pertinence." (3) Six pairs of "matched circles" in opposite directions on the CMB. Roukema, et.al. in this paper actually claimed to find these circles in the WMAP data.
- How do these three predictions hold up after Planck? (1) I think if you look at Figure 1 of this paper on the Planck results, you see that the quadrupole point (the first data point) is below the model, but the statistical significance of this is low, and always will be. The statistics are limited by the "cosmic variance effect", which basically means we only have one universe to measure. So I don't think we can draw any conclusions on this one way or the other. (2) The best fit curvature data from the above Planck paper, using all available data (not just Planck data), is a value of 1.000 +/- 0.005, so this would seem to rule out Luminet's model at 2σ, or at least say that, if Luminet's model is correct, the size of the recurrence is too large for us ever to observe. (3) In this paper from the Planck collaboration they searched for the matched circles and they say, " We do not find any statistically significant correlation of circle pairs in any map." So, it appears to me that there is no evidence that Luminet's beautiful idea applies in our universe.