BRIDGE NUMBER, HEEGAARD GENUS AND NON-INTEGRAL DEHN SURGERY

作者：Baker Kenneth L^*; Gordon Cameron; Luecke John

来源：Transactions of the American Mathematical Society, 2015, 367(8): 5753-5830.

We show there exists a linear function w: N -> N with the following property. Let K be a hyperbolic knot in a hyperbolic 3-manifold M admitting a non-longitudinal S-3 surgery. If K is put into thin position with respect to a strongly irreducible, genus g Heegaard splitting of M, then K intersects a thick level at most 2w(g) times. Typically, this shows that the bridge number of K with respect to this Heegaard splitting is at most w(g), and the tunnel number of K is at most w(g) + g - 1.

• 出版日期2015-8