I made some sentences both using Inversion and not Inverion. Please check these out.
1After I had finished my work, I fell asleep. → Having finished my work, I fell asleep.
2I have little thought about the problem.→Little have I thought about the problem.
Thanks for your reply 5. However, I'm not sure that you understood what I asked about. I'll try it illustrate on an (hopefully) clearer example:
He fell asleep after he closed his eyes. - here probably is a connection between falling asleep and closing his eyes. You hardly ever fall asleep before or without closing your eyes.
He fell asleep after he had closed his eyes. - here probably is not a connection between falling asleep and closing his eyes. He might have done something between closing his eyes and falling asleep, such as taking a sleeping pill or something.
Is that true? Because that's what we were taught at the university where I study (at the department of linguistics). Nevertheless, my teachers have been known to be mistaken in the past.
I think you have a rather unnatural example there. Without more context, "He fell asleep after he closed his eyes" is not an utterance we encounter every day. Let's try a sentence that, I think, is more likely.
He wrote his novel after his wife (had) left him.
I do not think that either tense, past simple or past perfect, of itself implies that the leaving caused the writing.
What if I put the sentence like this:
He wrote his novel after his wife had left him.
And the question would be, does the statement suggest that there's no connection between his wife's leaving and his writing the novel?