Is Poincaré's conjecture related to CMB cosmology?

Discussion in 'Physics & Math' started by arfa brane, Jul 12, 2018 at 8:52 AM.

  1. arfa brane call me arf Valued Senior Member

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    --https://mathoverflow.net/questions/9708/poincaré-conjecture-and-the-shape-of-the-universe
     
    Last edited: Jul 12, 2018 at 9:19 AM
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  3. someguy1 Registered Senior Member

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    Wow it's a long long way from the type of math done by Perelman and anything going on in the physical world. And even if there is a relationship, we're a long long way from understanding it.

    More confusion of math with physics. There is so much of it going around these days.

    Thanks for the link. Definitely a question that's interesting whether or not it's true.

    ps -- Wow I read through the MathOverflow page. Very impressive. I think I did find some support in there for my opinion that the question's essentially meaningless. But a lot of smart people take it seriously. It's interesting how they apply higher topology and even algebraic topology to the universe. Now that's amazing.
     
    Last edited: Jul 16, 2018 at 2:03 AM
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  5. arfa brane call me arf Valued Senior Member

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    One of the reasons I looked at Poincaré's conjecture was because of heyuhua's posts about Yang's work. The question I asked myself was, what does the value of the Einstein constant have to do with geometry?

    I understand you get a factor of 4π in Gauss's formula because the divergence of potential is spherically symmetric (you sum over all directions, i.e. over all the surface of the spherical volume). Now Wikipedia tells me: "the Ricci flow may be defined by the geometric evolution equation[3]


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    . . . and there's that factor of -2, a point of contention in that (surprisingly uneducating) thread of heyuhua's.

    Or perhaps I'm looking at nothing significant .
     
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  7. arfa brane call me arf Valued Senior Member

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    -https://en.wikipedia.org/wiki/Ricci_flow

    But anyway, I object to Yang's EFE "solution" Guv = 4πGTuv because the EFE is written in tensor notation (describes a sum of tensor components); there are two indices which is why the constant is 8πG (up to a sign), in the "real" world we have tensors with single indices (i.e. vectors).
     

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