Timeline for Are the Euler Characteristics of noncollapsed manifolds with bounded Ricci curvature uniformly bounded above?
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| when toggle format | what | by | license | comment | |
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| Nov 30, 2017 at 3:00 | answer | added | Vitali Kapovitch | timeline score: 3 | |
| Nov 29, 2017 at 14:36 | comment | added | asv | Probably you aware of this, but let me notice that it was shown by G. Perelman that the connected sum of any number of $\mathbb{C}\mathbb{P}^2$ (which has arbitrarily large Euler characteristic) carries a Riemannian metric with positive Ricci curvature, diameter 1 and volume bounded away from 0. See his paper "Construction of manifolds of positive Ricci curvature with big volume and large Betti numbers" (1997). | |
| Nov 29, 2017 at 14:34 | comment | added | Jason Starr | For your first question, consider the case that $n$ equals $6$. Since we do not know whether there are only finitely many deformation types of Calabi-Yau manifolds of complex dimension $3$, it seems unlikely that we can bound the set of possible Euler characteristics. | |
| Nov 29, 2017 at 14:19 | history | asked | mathmetricgeometry | CC BY-SA 3.0 |