Timeline for Non-collapsed Alexandrov spaces, level surface of regular map homeo to its lifting?
Current License: CC BY-SA 4.0
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| Jun 16, 2019 at 13:46 | comment | added | mathmetricgeometry | @AntonPetrunin: The definition of regular map in Perelman's paper Alexandrov II is weaker than Elements of Morse theory. In Alexandrov II, for sets $A_i$, $\angle (A_i')_p, (A_j')_p >\frac{\pi}{2}-\delta$ and there is $\xi_p \in \Sigma_p$ such that $\angle (A_i')_p, \xi_p >\frac{\pi}{2}+\epsilon$. Let $f=(dist(A_1,\cdot),...)$, So you mean for i large, the level sets $f_i^{-1}(c)$ is homeomorphic to $f_i^{-1}(c)$? | |
| Jun 14, 2019 at 12:01 | comment | added | Anton Petrunin | The strongest version of stability theorem is given here anton-petrunin.github.io/papers/alexandrov/…. If I remember correctly, the statement you are looking for is there. (In the published paper Perelman simplified the proof, but made statements less general.) | |
| May 23, 2019 at 16:18 | history | asked | mathmetricgeometry | CC BY-SA 4.0 |