Abstract
Suppose is a closed irreducible orientable 3–manifold, is a knot in , and are bridge surfaces for and is not removable with respect to . We show that either is equivalent to or . If is not a 2–bridge knot, then the result holds even if is removable with respect to . As a corollary we show that if a knot in has high distance with respect to some bridge sphere and low bridge number, then the knot has a unique minimal bridge position.
Citation
Maggy Tomova. "Multiple bridge surfaces restrict knot distance." Algebr. Geom. Topol. 7 (2) 957 - 1006, 2007. https://doi.org/10.2140/agt.2007.7.957
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