<human>: My bf and I have been dating for a year now. My bf dated his ex a year and a half before we met. After they broke up, she came out as a lesbian. My bf was distraught by the break up, deleted his facebook, and moved to a new city. 

When we first started dating, he didn't seem to be hung up on his ex. He would make little comments here and there mentioning a story about an ex, but it seemed like normal reminiscing. After a few months, he started talking about his ex a lot more, but this was hard to avoid as he and she were involved with the same crowd of people. At one point, he mentioned to a friend that his ex recently got engaged. He seemed kind of incredulous, but not quite upset.

I think I have a really hard time pinpointing the exact instances that make me wary because I usually let issues fester in the hopes that they'll resolve themselves or I'll forget about them. But I've got an overall gut feeling that's leaving me feeling kinda bad. 

I directly asked him if he was still hung up on his ex and he answered that he was not. But, the other day, he was showing me something on facebook and her name popped up on the search results, about the fifth one from the top.

Can you give me a shortened version of the text?
<bot>: My bf may or may not be hung up on his ex. I'm not worried that he's going to leave me for her, but what are the implications for our relationship?