Geodesic
Bridge number and tangle products
Blair, Ryan1
1Department of Mathematics, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia PA 19104, USA
Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 1125-1141
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

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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.

DOI : 10.2140/agt.2013.13.1125
Classification : 57M25, 57M27, 57M50
Keywords: Knot, bridge number, product, surface

Blair, Ryan  1

1 Department of Mathematics, David Rittenhouse Lab, 209 South 33rd Street, Philadelphia PA 19104, USA 
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Blair, Ryan. Bridge number and tangle products. Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 1125-1141. doi: 10.2140/agt.2013.13.1125

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