Obtaining genus 2 Heegaard splittings from Dehn surgery

@article{Baker2013ObtainingG2,
  title={Obtaining genus 2 Heegaard splittings from Dehn surgery},
  author={Kenneth L. Baker and Cameron McA. Gordon and John S Luecke},
  journal={Algebraic \& Geometric Topology},
  year={2013},
  volume={13},
  pages={2471-2634}
}
Let K' be a hyperbolic knot in S^3 and suppose that some Dehn surgery on K' with distance at least 3 from the meridian yields a 3-manifold M of Heegaard genus 2. We show that if M does not contain an embedded Dyck's surface (the closed non-orientable surface of Euler characteristic -1), then the knot dual to the surgery is either 0-bridge or 1-bridge with respect to a genus 2 Heegaard splitting of M. In the case M does contain an embedded Dyck's surface, we obtain similar results. As a… 
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