Bridge number and tangle products

Details Bridge number and tangle products Bridge number and tangle products

2011-08-29

arxiv.org/abs/1108.5640v1

Mathematics

Geometric Topology

13 pages, 11 figures

Scientific paper

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.

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