Generally, I have been very satisfied with the stack exchanges, but on occasion I run into a problem like this. I am trying to understand the significance of the transition functions of a manifold being differentiable. The answers give a very nice explanation for what the transition functions represent, but they all end with a very informal reason for showing that a differentiable transition function implies a derivative can be defined. They appeal to intuition that just does not convince me of the result.
Here are some things I could do (and where they could go wrong):
- Try to rephrase the question so it is not identical. (Seems vulnerable to being related enough that it would be flagged as a duplicate.)
- Ask on the chat room. (Tried it. No one answered.)
- Repeat option 2 until I get an answer. (I suppose if there is a nonzero probability of getting an answer for a given attempt, as the number of tries approaches infinity I am guaranteed an answer eventually.)
- Leave a comment on one of the answers to where the original question is posted. (The question was last active 11 months ago so it seems unlikely that anyone would respond.)
- Abandon hope. It was asked and answered. Try to find another site.
What would you recommend I do in this situation?