Timeline for Stability for open manifolds of finite volume under lower Ricci curvature bound
Current License: CC BY-SA 3.0
9 events
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| Jan 15, 2016 at 1:32 | comment | added | J. GE | I was really interested in exotic smooth structures, so let's assume $N_i$ and $M$ are all homeomorphic at the beginning. | |
| Jan 15, 2016 at 1:29 | comment | added | Igor Belegradek | In the pointed case there are counterexamples, coming from e.g. cusp opening of hyperbolic manifolds of dimension 2 and 3: closed hyperbolic manifolds can converge to noncompact hyperbolic manifolds of finite volume. I do not undertand what you said about moving the basepoint and preventing collapse. | |
| Jan 15, 2016 at 1:12 | comment | added | J. GE | @IgorBelegradek, I mean global, unpointed. But for pointed version, you have counterexample? moving the center point to infinity can prevent manifold from collapsing in finite volume case? | |
| Jan 15, 2016 at 0:59 | comment | added | Igor Belegradek | The question is still unclear: did you mean pointed GH convergence or unpointed GH convergence? | |
| Jan 15, 2016 at 0:39 | history | edited | J. GE | CC BY-SA 3.0 |
edited title
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| Jan 14, 2016 at 23:42 | history | edited | J. GE | CC BY-SA 3.0 |
added 71 characters in body
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| Jan 14, 2016 at 23:41 | comment | added | J. GE | @IgorBelegradek, thanks, the $\to$ means GH convergence. Yes, you are right, I need to exclude the tangent cone here, so what if all $N_i$ and $M$ are of finite volume? | |
| Jan 14, 2016 at 18:06 | comment | added | Igor Belegradek | What do you mean by $N_i\to M$ for open manifolds? If you mean pointed GH convergence, then let $N_i$ be the fixed metric on $N$ rescaled by $i$, so that the limit is a Euclidean space, which need not homeomorphic to $N$. | |
| Jan 14, 2016 at 17:55 | history | asked | J. GE | CC BY-SA 3.0 |