Timeline for Topological rigidity of cartesian product with $\mathbb{R}$
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Oct 9 at 2:55 | comment | added | Moishe Kohan | Did you understand the answer? | |
| Sep 18 at 6:56 | comment | added | Michael Albanese | As pointed out, you cannot conclude that $V$ and $W$ are diffeomorphic. However, if $V$ and $W$ are closed, they must be h-cobordant, see here. | |
| Sep 18 at 3:12 | answer | added | Moishe Kohan | timeline score: 4 | |
| Sep 17 at 13:17 | comment | added | Moishe Kohan | This is false: one uses existence of h-cobordant nonhomeomorphic manifolds to prove it by stacking together infinitely many such cobordisms. | |
| Sep 17 at 7:22 | comment | added | Gro-Tsen | Let me just comment in passing that this isn't true without the “compact” hypothesis: if $V=\mathbb{R}^4$ and $W$ is an exotic $\mathbb{R}^4$, then $V\times\mathbb{R}$ and $W\times\mathbb{R}$ are both the standard $\mathbb{R}^5$. | |
| Sep 17 at 5:35 | comment | added | Christophe Raffalli | Thanks for you help Ryan, you might be right too! I am not expert in that field... | |
| Sep 17 at 5:33 | comment | added | Ryan Budney | I'll think about it again in the morning. What I said might be nonsense, I'm tired. | |
| Sep 17 at 5:31 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Fully Math Jaxed
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| Sep 17 at 5:25 | history | edited | Christophe Raffalli | CC BY-SA 4.0 |
added 3 characters in body
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| Sep 17 at 5:18 | history | edited | Christophe Raffalli | CC BY-SA 4.0 |
added 3 characters in body
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| Sep 17 at 5:17 | comment | added | Christophe Raffalli | And topological is may be a bit to weak. My manifold are DIFF. I edit the post. | |
| Sep 17 at 5:11 | comment | added | Christophe Raffalli | Can you elaborate, the only counter example I see from whitehead is with V and W non compact (and in fact non simply connected at infinity). | |
| Sep 17 at 5:07 | comment | added | Ryan Budney | Off the top of my head I suspect that result isn't true. Presumably if you're in the dimensions where s-cobordism applies it would fail when the Whitehead group of the fundamental group is non-trivial. | |
| Sep 17 at 4:57 | history | edited | Christophe Raffalli | CC BY-SA 4.0 |
edited body
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| Sep 17 at 4:36 | history | edited | David Roberts♦ |
edited tags
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| S Sep 17 at 2:47 | review | First questions | |||
| Sep 17 at 5:31 | |||||
| S Sep 17 at 2:47 | history | asked | Christophe Raffalli | CC BY-SA 4.0 |