What does Henry Dobbins carry, what does he do with it, and why does he still keep it even after his girlfriend dumps him?

Henry Dobbins carries his girlfriend's pantyhose. He keeps them tied around his neck, supposedly for good luck. Ironically, he continues wearing the pantyhose even after she dumps him, saying that they're still lucky. Maybe he likes the way they feel around his neck. Or maybe he the pantyhose are simply his strongest connection to home, and he is unwilling to let go of how they have made him feel.