Abstract
In a 3–manifold M, let K be a knot and R be an annulus which meets K transversely. We define the notion of the pair (R, K) being caught by a surface Q in the exterior of the link K ∪ ∂ R. For a caught pair (R, K), we consider the knot Kn gotten by twisting Kn times along R and give a lower bound on the bridge number of Kn with respect to Heegaard splittings of M; as a function of n, the genus of the splitting, and the catching surface Q. As a result, the bridge number of Kn tends to infinity with n. In application, we look at a family of knots {Kn} found by Teragaito that live in a small Seifert fiber space M and where each Kn admits a Dehn surgery giving S3. We show that the bridge number of Kn with respect to any genus-2 Heegaard splitting of M tends to infinity with n. This contrasts with other work of the authors as well as with the conjectured picture for knots in lens spaces that admit Dehn surgeries giving S3
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1-40 |
| Number of pages | 40 |
| Journal | Algebraic and Geometric Topology |
| Volume | 16 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 23 2016 |
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ASJC Scopus subject areas
- Geometry and Topology
Cite this
Bridge number and integral Dehn surgery. / Baker, Kenneth; Gordon, Cameron; Luecke, John.
In: Algebraic and Geometric Topology, Vol. 16, No. 1, 23.02.2016, p. 1-40.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Bridge number and integral Dehn surgery
AU - Baker, Kenneth
AU - Gordon, Cameron
AU - Luecke, John
PY - 2016/2/23
Y1 - 2016/2/23
N2 - In a 3–manifold M, let K be a knot and R be an annulus which meets K transversely. We define the notion of the pair (R, K) being caught by a surface Q in the exterior of the link K ∪ ∂ R. For a caught pair (R, K), we consider the knot Kn gotten by twisting Kn times along R and give a lower bound on the bridge number of Kn with respect to Heegaard splittings of M; as a function of n, the genus of the splitting, and the catching surface Q. As a result, the bridge number of Kn tends to infinity with n. In application, we look at a family of knots {Kn} found by Teragaito that live in a small Seifert fiber space M and where each Kn admits a Dehn surgery giving S3. We show that the bridge number of Kn with respect to any genus-2 Heegaard splitting of M tends to infinity with n. This contrasts with other work of the authors as well as with the conjectured picture for knots in lens spaces that admit Dehn surgeries giving S3
AB - In a 3–manifold M, let K be a knot and R be an annulus which meets K transversely. We define the notion of the pair (R, K) being caught by a surface Q in the exterior of the link K ∪ ∂ R. For a caught pair (R, K), we consider the knot Kn gotten by twisting Kn times along R and give a lower bound on the bridge number of Kn with respect to Heegaard splittings of M; as a function of n, the genus of the splitting, and the catching surface Q. As a result, the bridge number of Kn tends to infinity with n. In application, we look at a family of knots {Kn} found by Teragaito that live in a small Seifert fiber space M and where each Kn admits a Dehn surgery giving S3. We show that the bridge number of Kn with respect to any genus-2 Heegaard splitting of M tends to infinity with n. This contrasts with other work of the authors as well as with the conjectured picture for knots in lens spaces that admit Dehn surgeries giving S3
UR - http://www.scopus.com/inward/record.url?scp=84960089337&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84960089337&partnerID=8YFLogxK
U2 - 10.2140/agt.2016.16.1
DO - 10.2140/agt.2016.16.1
M3 - Article
AN - SCOPUS:84960089337
VL - 16
SP - 1
EP - 40
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
SN - 1472-2747
IS - 1
ER -