Timeline for $\mathbb RP^n$ bundles over the circle, II
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Jan 24, 2022 at 17:21 | history | edited | Jens Reinhold | CC BY-SA 4.0 |
Fixed small issue with definition of homomorphism
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| Jan 24, 2022 at 7:14 | comment | added | Nicolast | This is not going to change much of your discussion, but I don't think there is a continuous homomorphism from $\mathrm{Diff}(\mathbb RP^n)$ to $\mathrm{Diff}(\mathbb S^n)$ for odd $n$ because every diffeomorphism of $\mathbb RP^n$ has two lifts in $\mathbb S^n$, and you cannot choose one continuously. However, the group of diffeomorphisms of $\mathbb S^n$ that factor to $\mathbb R P^n$ is a double cover of $\mathrm{Diff} (\mathbb R P^n)$. For $n$ even this cover is trivial so it admits a section, and for $n$ odd it is non-trivial, hence induces an isomorphism of connected components. | |
| Jan 23, 2022 at 16:40 | history | asked | Jens Reinhold | CC BY-SA 4.0 |