Abstract
Let be a hyperbolic knot in and suppose that some Dehn surgery on with distance at least from the meridian yields a –manifold of Heegaard genus . We show that if does not contain an embedded Dyck’s surface (the closed nonorientable surface of Euler characteristic ), then the knot dual to the surgery is either –bridge or –bridge with respect to a genus Heegaard splitting of . In the case that does contain an embedded Dyck’s surface, we obtain similar results. As a corollary, if does not contain an incompressible genus surface, then the tunnel number of is at most .
Citation
Kenneth L Baker. Cameron Gordon. John Luecke. "Obtaining genus $2$ Heegaard splittings from Dehn surgery." Algebr. Geom. Topol. 13 (5) 2471 - 2634, 2013. https://doi.org/10.2140/agt.2013.13.2471
Information