Abstract
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 S3 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.
Original language | English (US) |
---|---|
Pages (from-to) | 5753-5830 |
Number of pages | 78 |
Journal | Transactions of the American Mathematical Society |
Volume | 367 |
Issue number | 8 |
DOIs | |
State | Published - 2015 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics