TY - JOUR

T1 - Bridge number and integral Dehn surgery

AU - Baker, Kenneth L.

AU - Gordon, Cameron

AU - Luecke, John

N1 - Publisher Copyright:
© 2016, Science in China Press. All rights reserved.

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

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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 -