"Again, this is demonstrably false; DrGreg provided a very detailed counter example.
Starting from the same point the components of the final parallel-transported vector are in fact changed depending on the path. This is fundamental to understanding the very basic concept of curvature, and instead of trying to learn it you are just going around in circles making the same false assertion over and over."
Dalespam, Thread 35
This "demonstrably false" notion arises out of the fact that the singularities north and south poles have been chosen simultaneously.I have demonstrated my reason as to why they should not be chosen simultaneously in thread #15 ,http://physicsforums.com/showpost.ph...8&postcount=15
If you chop off either the north or the south pole from the sphere the demonstration provided by Dr Greg fails