Timeline for Do Gromov hyperbolic spaces admit concical geodesic bicombings?
Current License: CC BY-SA 4.0
15 events
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| Sep 19, 2023 at 0:19 | history | became hot network question | |||
| Sep 18, 2023 at 19:32 | comment | added | Math_Newbie | Thanks Moise. I also have some doubts due to this article: arxiv.org/abs/2106.12681 In the final section, the authors cast doubt on the existence of a conical bicombing (even in a simple case) | |
| Sep 18, 2023 at 19:31 | vote | accept | Math_Newbie | ||
| Sep 18, 2023 at 18:06 | answer | added | Moishe Kohan | timeline score: 2 | |
| Sep 18, 2023 at 17:33 | comment | added | Moishe Kohan | As I explained, the added assumptions are insufficient. Maybe you should explain in detail the actual example you are interested in. | |
| Sep 18, 2023 at 17:16 | comment | added | Math_Newbie | @MoisheKohan Fair, I'm also assuming its a polish space. In fact, its a specific remetrization of the hyperspace of compact subsets of a finite-dimensional closed convex subset of a Banach space. This: sciencedirect.com/science/article/pii/S0022247X16301007 But in particular (i added this since it is important) it is polish. | |
| Sep 18, 2023 at 17:15 | history | edited | Math_Newbie | CC BY-SA 4.0 |
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| Sep 18, 2023 at 16:54 | comment | added | Moishe Kohan | Ok, there is still an easy counter-example: take the unit sphere with the standard (Riemannian) metric and remove a point from it. Maybe you are making further assumptions to rule out such examples. Note that metric completeness is not enough (remove a small open disk from the unit sphere). | |
| Sep 18, 2023 at 16:47 | comment | added | Math_Newbie | @MoisheKohan Ah, in the case I had in mind, my space is a contracible ANR which is additionally $\delta$-hyperbolic. Otherwise, yes, I would not have a shot. | |
| Sep 18, 2023 at 16:46 | history | edited | Math_Newbie | CC BY-SA 4.0 |
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| Sep 18, 2023 at 16:31 | history | edited | Math_Newbie | CC BY-SA 4.0 |
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| Sep 18, 2023 at 16:29 | comment | added | YCor | I think you should write "Gromov-hyperbolic" rather than $\delta$-hyperbolic. $\delta$ is a parameter, which does not play any role in your question. | |
| Sep 18, 2023 at 16:28 | history | edited | YCor | CC BY-SA 4.0 |
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| Sep 18, 2023 at 16:28 | comment | added | Moishe Kohan | This condition implies contractibility of $X$, are you sure that you really mean it? | |
| Sep 18, 2023 at 16:18 | history | asked | Math_Newbie | CC BY-SA 4.0 |