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Filling knots and essential geodesic systole
We prove that every closed, orientable $3$--manifold contains hyperbolic knots with arbitrarily large essential geodesic systole. That is, for any $3$--manifold $M$, and $R> 0$ there is a hyperbolic knot $K \subset M$ such that every closed geodesic in the knot complement which is non-null-homotopic
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