Universal surgery bounds on hyperbolic 3-manifolds

AbstractWe investigate Dehn surgery in relation to the injectivity radius of a closed hyperbolic 3-manifold M. We show that the injectivity radius has global implications for the topology of M by obtaining some universal restrictions, characterised by inj(M), on the possible surgery descriptions of M. In particular, we show that provided inj(M) is sufficiently large, then M cannot be obtained by p/q surgery on a knot in S3 with |q|>4