Why are we talking about topology? In E17, I like to have a number of virtual desktops, and I like them to be all connected to each other so I can flip between them by pushing on the edge of the screen. FVWM did this years ago, and I always liked the idea. E17 also supports wrapping of virtual desktops, so you end up with something like this:
My laptop uses a three by three grid, but it's the same thing. |
Now, at work, I have a dual monitor setup, and I assumed this would just work the same, but with fat desktops. However, I discovered upon getting everything configured that it's actually this far more complicated thing:
Green arrows are bidirectional, as they were above. Orange are unidirectional. |
I don't have proof (again, see "worst math"), but I believe this defines a very oddly connected hollow torus. I don't know how you construct a unidirectional connection in topology, but assuming that's valid, you basically have some sorted of ratcheted torus for each monitor: you can travel poloidally unobstructed (corresponding to vertical shifts), but can only travel in one direction toroidally. Switching between monitors is then functionally equivalent to passing through the ratchet onto the other side of the torus. There's some ambiguity, since you can then shift each monitor separately, so where you come out on the other side of the torus isn't a priori obvious, but I think the bulk of the thing is sorted.
Anyway, I thought it was cool, and now my already-confusing-to-other-people desktop is going to get more confusing.