Timeline for The diameter of the projection of a convex core
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| May 29 at 5:16 | vote | accept | yanqing | ||
| May 29 at 2:31 | answer | added | Ian Agol | timeline score: 4 | |
| May 29 at 2:07 | comment | added | Ian Agol | @yanqing: No, this construction will be compressible only from one side. | |
| May 25 at 6:23 | comment | added | yanqing | Thank you, Ian. If I understand your example correctly, $\partial N$ is compressible from both sides. May I ask that: will the diameter of $N$ be bounded by the diameter of $\partial N$ if $\partial N$ is separating and incompressible from one side? | |
| May 23 at 18:55 | comment | added | Ian Agol | No, this won’t hold in general. One may construct manifolds with $\pi(N)$ of unbounded diameter and $\pi(\partial N)$ bounded diameter. I might try to write a more complete answer, but to summarize: one may take a hyperbolic handlebody with convex core $N$ and $\partial N$ of bounded diameter but $N$ of arbitrarily large diameter. Perturb a bit so that one may extend by a reflection group using Thurston’s reflection trick, then a manifold cover will have $N$ embedded and hence won’t satisfy your conditions. | |
| May 21 at 22:18 | history | edited | yanqing | CC BY-SA 4.0 |
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| May 21 at 22:18 | comment | added | yanqing | Sorry, I should delete the regular hypothesis. | |
| May 21 at 20:18 | comment | added | HJRW | So presumably you want to delete the “regular” hypothesis too? | |
| May 21 at 15:22 | review | Close votes | |||
| Jun 5 at 3:02 | |||||
| May 21 at 6:40 | history | edited | yanqing | CC BY-SA 4.0 |
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| May 21 at 5:42 | comment | added | HJRW | Also, since $M$ is closed, all diameters in $M$ are finite. | |
| May 21 at 5:36 | comment | added | HJRW | It can’t be a regular cover. Any finitely generated non-trivial normal subgroup of $\pi_1(M)$ is a closed surface group or a 3-manifold group. | |
| May 21 at 5:17 | history | asked | yanqing | CC BY-SA 4.0 |