Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 16, Number 1 (2016), 1-40.
Bridge number and integral Dehn surgery
In a –manifold , let be a knot and be an annulus which meets transversely. We define the notion of the pair being caught by a surface in the exterior of the link . For a caught pair , we consider the knot gotten by twisting times along and give a lower bound on the bridge number of with respect to Heegaard splittings of ; as a function of , the genus of the splitting, and the catching surface . As a result, the bridge number of tends to infinity with . In application, we look at a family of knots found by Teragaito that live in a small Seifert fiber space and where each admits a Dehn surgery giving . We show that the bridge number of with respect to any genus- Heegaard splitting of tends to infinity with . 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 .
Algebr. Geom. Topol., Volume 16, Number 1 (2016), 1-40.
Received: 20 December 2013
Revised: 11 February 2015
Accepted: 26 April 2015
First available in Project Euclid: 16 November 2017
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Baker, Kenneth L; Gordon, Cameron; Luecke, John. Bridge number and integral Dehn surgery. Algebr. Geom. Topol. 16 (2016), no. 1, 1--40. doi:10.2140/agt.2016.16.1. https://projecteuclid.org/euclid.agt/1510841103