Given a finitely presented group $G$, how many necessary conditions do people know for $G$ to be isomorphic to the fundamental group of some closed connected 3-manifold? (e.g. residually finite)



Judging whether a finitely presented group is a 3-manifold group?
Apologies for the shameless self-promotion, but as you ask for *necessary* conditions, you seem to want a list of theorems of the form 'If G is a 3-manifold group then G has property P'.


Aschenbrenner, Friedl and I have given what I think is a pretty exhaustive list in our survey paper [here](http://arxiv.org/abs/1205.0202).


