## Examples of 3-manifolds with RFRS fundamental group

I'm wondering if anyone knows how to construct hyperbolic 3-manifolds whose fundamental group is RFRS. Clearly the recent work of Agol, Wise, etc. says that such manifolds are abundant, and in particular present in every commensurability class. But how do you construct examples?

The only examples of RFRS manifolds that I'm aware of are torus knot complements (thanks to Stefan Friedl for pointing this out), but these are of course non-hyperbolic.

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FYI, there's an error in my original paper. I stated that knot complements cannot be RFRS, but this is false e.g. for torus knots. A necessary condition is that Alexander polynomial has cyclotomic factors. Also, RAAGs are RFRS, and there are some graph 3-manifolds which are RAAGs when the defining graph is a tree (or $T^3$). – Agol Oct 19 at 4:00

So take your favourite right-angled reflection group $\Gamma$ in $\mathbb{H}^3$ and take the commutator subgroup $[\Gamma,\Gamma]$ (which is always torsion-free, as all the torsion injects into $H_1$). This will give you an example.