Volume 10, issue 2 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Bridge number and Conway products

Ryan C Blair

Algebraic & Geometric Topology 10 (2010) 789–823
Abstract

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.

Keywords
bridge position, knot, Conway product
Mathematical Subject Classification 2000
Primary: 57M25, 57M27, 57M50
References
Publication
Received: 13 May 2009
Revised: 15 December 2009
Accepted: 30 January 2010
Published: 31 March 2010
Authors
Ryan C Blair
Department of Mathematics
University of California, Santa Barbara
Santa Barbara, CA 93106