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.
Citation
Ryan Blair. "Bridge number and tangle products." Algebr. Geom. Topol. 13 (2) 1125 - 1141, 2013. https://doi.org/10.2140/agt.2013.13.1125
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