# Tagged Questions

**1**

vote

**1**answer

268 views

### Kropholler's Conjecture and 3-manifolds

Suppose that $G$ is a group and that $H$ is a subgroup, both finitely generated, and assume that there is a non-trivial H-almost invariant set $X$ with $HXH=X$. Kropholler's Conjecture asserts that $ ...

**6**

votes

**3**answers

513 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

646 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

**1**answer

288 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 ...