Algebraic & Geometric Topology 7 (2007) 957–1006

DOI: 10.2140/agt.2007.7.957

Abstract

Suppose M is a closed irreducible orientable 3–manifold, K is a knot in M, P and Q are bridge surfaces for K and K is not removable with respect to Q. We show that either Q is equivalent to P or d(K,P)≤2-χ(Q-K). If K is not a 2–bridge knot, then the result holds even if K is removable with respect to Q. As a corollary we show that if a knot in S³ has high distance with respect to some bridge sphere and low bridge number, then the knot has a unique minimal bridge position.

Keywords

knot distance, bridge position, Heegaard splitting, strongly irreducible, weakly incompressible

Mathematical Subject Classification

Primary: 57M25, 57M27, 57M50

References

Publication

Received: 5 April 2007
Accepted: 7 May 2007
Published: 20 June 2007

Authors