Sign in
Multiple bridge surfaces restrict knot distance
Journal article   Open access  Peer reviewed

Multiple bridge surfaces restrict knot distance

Maggy Tomova
Algebraic & geometric topology, Vol.7(1), pp.957-1006
2007
DOI: 10.2140/agt.2007.7.957
url
https://doi.org/10.2140/agt.2007.7.957View
Published (Version of record) Open Access

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 − x(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.

Details

Metrics