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
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Baker, K., Gordon, C., & Luecke, J. (2015). Bridge number, Heegaard genus and non-integral dehn surgery. Transactions of the American Mathematical Society, 367(8), 5753-5830. https://doi.org/10.1090/S0002-9947-2014-06328-9