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 |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Bridge number, Heegaard genus and non-integral dehn surgery. / Baker, Kenneth; Gordon, Cameron; Luecke, John.
In: Transactions of the American Mathematical Society, Vol. 367, No. 8, 2015, p. 5753-5830.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Bridge number, Heegaard genus and non-integral dehn surgery
AU - Baker, Kenneth
AU - Gordon, Cameron
AU - Luecke, John
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84929448381&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84929448381&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-2014-06328-9
DO - 10.1090/S0002-9947-2014-06328-9
M3 - Article
AN - SCOPUS:84929448381
VL - 367
SP - 5753
EP - 5830
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 8
ER -