It sounds like MapLinkedList, the class, shouldn't hold references to other objects. It should be an instance of the class. Other than that it looks 'bout right.
Whoa there cowboy! Shouldn't ProcessMap be a method and not no class?
What does the MapManager have to do with the individual instances of Map objects? Why can't a Map think, be, and live for itself? How would you feel if you were a map and were granted no autonomy? Is that the kind of world you want to live in? Is that how you intend to raise our kids? And I call you a friend, even a lover? Puff! Not after today: Your design makes no sense, you need to go back to CS1322. And more than that, I can't be with someone who doesn't know how to design.
If we are in analysis what would be wrong with names like MapLinkedList? Barbara Ericson