Timeline for Smooth map homotopic to Lie group homomorphism
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 7, 2020 at 3:25 | history | became hot network question | |||
| Jul 7, 2020 at 1:56 | answer | added | Jason DeVito - on hiatus | timeline score: 9 | |
| Jul 7, 2020 at 1:51 | vote | accept | Hang | ||
| Jul 6, 2020 at 20:40 | comment | added | Tyrone | @NajibIdrissi $SO(4)$ and $S^3\times SO(3)$. It is true however that if $G,G'$ are connected simple lie groups, then $G,G'$ are isomorphic if and only if they are homotopy equivalent. | |
| Jul 6, 2020 at 20:35 | answer | added | Igor Belegradek | timeline score: 22 | |
| Jul 6, 2020 at 20:33 | comment | added | Najib Idrissi | @ConnorMalin Don't all such examples need to be disconnected? | |
| Jul 6, 2020 at 20:28 | comment | added | Connor Malin | A non connected example of this is given by $H= \mathbb{Z}/2 \times \mathbb{Z}/2$ and $G= \mathbb{Z}/4$. | |
| Jul 6, 2020 at 20:17 | comment | added | Connor Malin | If you construct two Lie groups such that $H \simeq G$, but $BH \not\simeq BG$ then any homotopy equivalence $H \simeq G$ cannot be homotopic to a homomorphism, since applying $B$ to it would deloop it to a weak equivalence. | |
| Jul 6, 2020 at 19:47 | history | edited | Hang | CC BY-SA 4.0 |
added 10 characters in body
|
| Jul 6, 2020 at 19:44 | answer | added | Josh Lackman | timeline score: 6 | |
| Jul 6, 2020 at 19:23 | history | asked | Hang | CC BY-SA 4.0 |