09-11-2016, 11:34 PM

Ok, maybe I figured it out. First, consider a simply connected space, such as S^3. Suppose there's a path through it, point A to point B. Now traverse it in reverse, point B back to point A. That's a closed loop. Since the space is simply connected, it can be shrunk to a point - in particular, the identity of the space. So in this sense traversing the closed loop from A, to B, back to A, is equivalent to the identity. Therefore any path (A and B were of course arbitrarily chosen) is reversible.

But you can't do that with a connected space which is not simple, such as SO(3).

Is that what you're getting at?

But you can't do that with a connected space which is not simple, such as SO(3).

Is that what you're getting at?