Bridge number and tangle products

Blair, Ryan

doi:10.2140/agt.2013.13.1125

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Bridge number and tangle products

Ryan Blair

Algebraic & Geometric Topology 13 (2013) 1125–1141

DOI: 10.2140/agt.2013.13.1125

Abstract

We show that essential punctured spheres in the complement of links with distance three or greater bridge spheres have bounded complexity. We define the operation of tangle product, a generalization of both connected sum and Conway product. Finally, we use the bounded complexity of essential punctured spheres to show that the bridge number of a tangle product is at least the sum of the bridge numbers of the two factor links up to a constant error.

Keywords

Knot, bridge number, product, surface

Mathematical Subject Classification 2010

Primary: 57M25, 57M27, 57M50

References

Publication

Received: 21 January 2012

Revised: 6 June 2012

Accepted: 26 October 2012

Published: 17 April 2013

Authors

Ryan Blair
Department of Mathematics David Rittenhouse Lab 209 South 33rd Street Philadelphia PA 19104 USA
http://www.math.upenn.edu/~ryblair

Volume 13, issue 2 (2013)