Timeline for Synthetic projective lines
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 20, 2015 at 15:51 | answer | added | Tim Penttila | timeline score: 5 | |
| Nov 18, 2015 at 8:39 | history | edited | Tom De Medts |
added the tag incidence-geometry
|
|
| Nov 18, 2015 at 8:34 | answer | added | Tom De Medts | timeline score: 6 | |
| Nov 18, 2015 at 3:52 | vote | accept | Mike Shulman | ||
| Nov 15, 2015 at 23:21 | answer | added | Tim Penttila | timeline score: 8 | |
| Oct 18, 2015 at 4:15 | comment | added | Mike Shulman | @AllenKnutson That's similar to what I was thinking of. Note that once you've specified 0, 1, and $\infty$, you don't need to muck around with cross-ratios any more to get something projective; every point is already a single number, so you can just add and multiply them directly. This gives you some partial 5-ary operations, which can both be encoded using the functionality of the 6-ary "quadrangular hexad" relation. But at this point I'm mainly wondering whether anything like this has been done before; it seems a natural thing to try. | |
| Oct 17, 2015 at 3:18 | comment | added | Allen Knutson | Given 3 distinct and 4 distinct points in $\mathbb P^1$, we can use the first three to decide where $0$, $1$, $\infty$ are, and the latter four to specify a cross-ratio. That number should then be an 8th point. I have no idea what relations this 7-ary (partially defined) operation should satisfy. | |
| Oct 16, 2015 at 23:43 | answer | added | Gjergji Zaimi | timeline score: 5 | |
| Oct 16, 2015 at 6:41 | comment | added | Matthias Wendt | Something related to this might have been done in the theory of Moufang sets. (These are, more generally, related to algebraic groups of rank one, but in particular the projective line with its $\operatorname{PGL}_2$-action is an example of a Moufang set.) Could be that some axioms exist that single out the projective lines among the wild world of Moufang sets... | |
| Oct 16, 2015 at 3:43 | history | asked | Mike Shulman | CC BY-SA 3.0 |