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Poincaré, Ricci flow and Super String Theory

  1. Jul 7, 2004 #1
    I just read the latest Scientific American and they have an article about the proof of the Poincaré conjecture. Apparently the proof uses a modified (an extra element) Ricci flow and then the article says that the modification to the Ricci flow pops up in Super String Theory :confused: .

    Does this relate to the Calabi-Yau manifolds and their possible transformations? How? Is it relevant to String Theory?
  2. jcsd
  3. Jul 9, 2004 #2
    First off, I believe what is being described is a 3-manifold (3-sphere for the topologist) where I BELIEVE a Calabi-Yau manifold is a 6-manifold. (I may be mistaken).

    Secondly, I believe Perelman, when modifying the Ricci flow equation, added a term to the equation. I do believe that this term is often used in string theories.

    Still, it very well may be applicable to ST.

    Paden Roder
  4. Jul 9, 2004 #3
  5. Jul 10, 2004 #4
    Don't know squat about strings but i am curretly (slowly) reading the Perleman papers. There is a ricci like analogue for the renormalization "group" flow in some qft models....no idea if it comes up in string theory.
    Mike Anderson has a nice page of notes on the proof and background....maybe that will help you:


    And this was the first overview of the papers from the period after the publication of the results:

    Also, i am not sure how they are viewed/used in string theory but i have always seen calabi Yau spaces defined as 2n dim manifolds with SU(n) holonomy.
    So though 6 might be reasonable i see no compelling reason that it is the only dimension.

    If you should find out the connection to strings please let us know.
    Last edited: Jul 10, 2004
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