Geodesic
Bridge number and Conway products
Blair, Ryan C1
1Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106
Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 789-823
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In this paper, we give a structure theorem for c-incompressible Conway spheres in link complements in terms of the standard height function on S3. We go on to define the generalized Conway product K1 ∗cK2 of two links K1 and K2. Provided K1 ∗cK2 satisfies minor additional hypotheses, we prove the lower bound β(K1 ∗cK2) ≥ β(K1) − 1 for the bridge number of the generalized Conway product where K1 is the distinguished factor. Finally, we present examples illustrating that this lower bound is tight.

DOI : 10.2140/agt.2010.10.789
Keywords: bridge position, knot, Conway product

Blair, Ryan C  1

1 Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA 93106 
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Blair, Ryan C. Bridge number and Conway products. Algebraic and Geometric Topology, Tome 10 (2010) no. 2, pp. 789-823. doi: 10.2140/agt.2010.10.789

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