Algebraic & Geometric Topology

Bridge number and Conway products

Ryan C Blair

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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 K1cK2 of two links K1 and K2. Provided K1cK2 satisfies minor additional hypotheses, we prove the lower bound β(K1cK2)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.

Article information

Algebr. Geom. Topol., Volume 10, Number 2 (2010), 789-823.

Received: 13 May 2009
Revised: 15 December 2009
Accepted: 30 January 2010
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds 57M50: Geometric structures on low-dimensional manifolds

bridge position knot Conway product


Blair, Ryan C. Bridge number and Conway products. Algebr. Geom. Topol. 10 (2010), no. 2, 789--823. doi:10.2140/agt.2010.10.789.

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