4‐free groups and hyperbolic geometry

We give new information about the geometry of closed, orientable hyperbolic 3‐manifolds with 4‐free fundamental group. As an application we show that such a manifold has volume greater than 3.44. This is in turn used to show that if M is a closed orientable hyperbolic 3‐manifold such that vol M⩽3.44, then dim⁡ℤ2 H1(M; ℤ2) ⩽ 7.

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