# Tagged Questions

**6**

votes

**3**answers

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

**2**answers

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:
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**6**

votes

**1**answer

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 ...