I am familiar with the result of Freedman that closed, simply connected four manifolds may be characterized up to homeomorphism by their intersection forms. This result is basically an extension of $h$-cobordism to dimension $4$ in the topological category.
I am wondering though if we remove the simply connected assumption, for what fundamental groups is there a known classification and in terms of what entities is the classification given?
Anecdotally I have heard that Freedman's classification can be generalized to other fundamental groups but cannot seem to find any documentation to support this.