Obtaining genus 2 Heegaard splittings from Dehn surgery
Abstract
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 3manifold M of Heegaard genus 2. We show that if M does not contain an embedded Dyck's surface (the closed nonorientable surface of Euler characteristic 1), then the knot dual to the surgery is either 0bridge or 1bridge 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 corollary, if M does not contain an incompressible genus 2 surface, then the tunnel number of K' is at most 2.
 Publication:

arXiv eprints
 Pub Date:
 April 2012
 arXiv:
 arXiv:1205.0049
 Bibcode:
 2012arXiv1205.0049B
 Keywords:

 Mathematics  Geometric Topology;
 57M27
 EPrint:
 127 pages, 81 figures