The topological explanation of Bohm-Aharonov effect assumes that the presence of a solenoid makes the configuration space non-simply connected.
- Now assume that the magnetic field inside the solenoid is switched off by turning off the current through it. However, the solenoid is still present but with $B=0$.
Does this situation correspond to a hole in space?
If yes, then the topological explanation, "presence of hole leads to a shift of the fringes" doesn't work. Because in this situation we don't observe a shift. If no, then the topological explanation works fine for me.
So should I conclude that there is no hole unless I turn on the magnetic field in the solenoid?