6
votes
3answers
500 views

Judging whether a finitely presented group is a 3-manifold group?

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)
5
votes
2answers
630 views

Residual Finiteness of Fundamental Group of Compact 3-Manifold

Hempel, in his 1987 article "Residual Finiteness for 3-Manifolds", shows that if $M$ is a compact Haken 3-manifold, then $\pi_1(M)$ is residually finite. The outline of the proof is basically: ...
6
votes
1answer
284 views

Residual finiteness for graph manifold groups

Is there a simple proof that 3-dimensional graph manifolds have residually finite fundamental groups? By "simple" I mean the proof that does not use any hard 3d topology. I care because I wish to ...