Hi @henryseg I made a mastodon account just to ask this question: For this cohomology fractal, is there a way to calculate the distance traveled if one were to take an infinitely zigzagging path from A to B to C?
@DoctorChunder I'm not sure if I understand your question... if you are travelling along the space-filling Cannon-Thurston map to get from A to B to C then I can't think of a way to interpret the question that doesn't give the answer "infinitely far". @saulsch
@DoctorChunder It is not clear what you mean by "infinitely zigzagging path from A to B to C". There are choices of path where the arclength is finite and can be computed, there are choices where the arclength is finite but cannot be computed, and there are choices where the arclength is infinite. As @henryseg points out, there is a particularly natural choice, namely using a subarc of the"Cannon-Thurston sphere filling curve", where the arclength is infinite.
Add comment