Timeline for Diffeomorphism groups of h-cobordant manifolds
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 4, 2022 at 21:58 | comment | added | skupers | No, it's at least about $\dim/3$ whatever the fundamental group. See Theorem 1.3.4 of the link. | |
| Apr 4, 2022 at 16:15 | comment | added | Ben Wieland | @skupers Since the manifold is not simply connected, isn't the stable range empty? | |
| Mar 30, 2022 at 16:07 | history | edited | Oscar Randal-Williams | CC BY-SA 4.0 |
Alert about a small mistake.
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| Feb 19, 2021 at 18:56 | comment | added | Connor Malin | Thanks for the response, I believe the embedding tower even predicts $B\mathrm{Diff}_\partial(M \times [0,1]) \simeq B\mathrm{Diff}_\partial(M' \times [0,1])$ , but I'm surprised it is accurate since it is codimension 0. | |
| Feb 19, 2021 at 17:03 | comment | added | skupers | In the pseudoisotopy stable range $\widetilde{\mathrm{Diff}}_\partial(M)/\mathrm{Diff}_\partial(M)$ is given by the $\mathbb{Z}/2$-orbits of the Whitehead spectrum of $M$, so going from $\widetilde{\mathrm{Diff}}$ to $\mathrm{Diff}$ is in a range only a question of extensions. This ought to be doable away from the prime 2 using Burghelea-Lashof. See Section 1.5 of arxiv.org/abs/math/0012101 for related results in the topological setting. | |
| Feb 19, 2021 at 16:47 | history | edited | Oscar Randal-Williams | CC BY-SA 4.0 |
added 721 characters in body
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| Feb 19, 2021 at 16:32 | history | answered | Oscar Randal-Williams | CC BY-SA 4.0 |