# Poincaré, Ricci flow and Super String Theory

1. Jul 7, 2004

### techwonder

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 .

Does this relate to the Calabi-Yau manifolds and their possible transformations? How? Is it relevant to String Theory?

2. Jul 9, 2004

### PRodQuanta

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.

3. Jul 9, 2004

### Jian

4. Jul 10, 2004

### styler

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:

http://www.math.sunysb.edu/%7Eanderson/papers.html

And this was the first overview of the papers from the period after the publication of the results:
http://www.math.lsa.umich.edu/research/ricciflow/overview102503.pdf

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