Why does following a tangent vector field visit all faces of the hypercube? Surely it’s not going to visit something like a dense subset of the hypersphere’s surface? (Or is it? My intuition comes from thinking about the torus)
My topology and maths are very rusty, am a software developer these days.
I think that there are both tangent vector fields that don’t and some that do. In the two dimnsional case (circle) certainly all do.
In n I intuitively would say that you should be able to have a vector field that does but I am now less confident to think about a proof on my bus rides while I answer here. I tried twice already.
I will try to think about this more, will ping here if I get more
Why does following a tangent vector field visit all faces of the hypercube? Surely it’s not going to visit something like a dense subset of the hypersphere’s surface? (Or is it? My intuition comes from thinking about the torus)
I’m more interested in the maths ;)
My topology and maths are very rusty, am a software developer these days.
I think that there are both tangent vector fields that don’t and some that do. In the two dimnsional case (circle) certainly all do.
In n I intuitively would say that you should be able to have a vector field that does but I am now less confident to think about a proof on my bus rides while I answer here. I tried twice already.
I will try to think about this more, will ping here if I get more