# What is known about a 3-manifold $M$ when its fundamental group is linear?

Suppose we have a 3-manifold $M$ and its respective fundamental group $\pi_1(M)$. An important question about its fundamental group is to ask if it is linear, i.e. they are isomorphic to a subgroup of the Lie group $GL(n,\mathbb{C})$. What is known about the manifold in such a case, i.e. what are the implications given the earlier question is correct? I am looking for references on any property, as asking for a specific one is too much to ask for. Your answers are greatly appreciated.

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Is there a 3-manifold whose fundamental group is known not to be linear? –  algori Oct 3 '12 at 22:24
As far as I know, there is not a 3-manifold with non-linear fundamental group. –  lagrangiansubmanifold Oct 3 '12 at 23:02