Geodesic
Multiple bridge surfaces restrict knot distance
Tomova, Maggy1
1Mathematics Department, Rice University, 6100 S Main Street, Houston TX 77005-1892, USA
Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 957-1006
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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.

DOI : 10.2140/agt.2007.7.957
Keywords: knot distance, bridge position, Heegaard splitting, strongly irreducible, weakly incompressible

Tomova, Maggy  1

1 Mathematics Department, Rice University, 6100 S Main Street, Houston TX 77005-1892, USA 
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Tomova, Maggy. Multiple bridge surfaces restrict knot distance. Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 957-1006. doi: 10.2140/agt.2007.7.957

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