Bridge number and tangle products

Ryan Blair

doi:10.2140/agt.2013.13.1125

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Home > Journals > Algebr. Geom. Topol. > Volume 13 > Issue 2 > Article

2013 Bridge number and tangle products

Ryan Blair

Algebr. Geom. Topol. 13(2): 1125-1141 (2013). DOI: 10.2140/agt.2013.13.1125

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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.