I don't think it's cheating. I still keep in touch with ex-girlfriends from long ago. There is no romance between us, but we are friends. I could understand a new girlfriend being jealous of my old exs if they were insecure about the relationship. Maybe this is the problem, your boyfriend is insecure with your relationship.
If you don't talk to the exs or even write to them, satisfying your curiosity about what has happened to them is normal. Find out why your boyfriend is insecure, and help him see that he can trust you. Maybe you give off some signals that he's replaceable. Or maybe you were already in a relationship when you two met, and he thinks that could happen again. Maybe it's happened to him before that someone cheated on him and he's afraid it will happen again.