Ryan Blair
Published 2011-08-29Version 1
We show that essential punctured spheres in the complement of links with distance three 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.
Comments: 13 pages, 11 figures
Independence of volume and genus $g$ bridge numbers
Wirtinger systems of generators of knot groups
Bridge number and integral Dehn surgery
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