|Affiliation||Nara Women's University|
|Time||Jan 9 17:10~17:30|
|Title||On the distance of bridge spheres for knots|
Distance of Heegaard splitting introduced by Hempel has been extended to apply to bridge surface, and has been studied by several authors. For example, for a knot $K$ in a closed 3-manifold, Tomova shows that either two bridge surfaces $P$, $Q$ for $K$ are equivalent or the distance $d(P, K)$ is at most $2-χ(Q-K)$. In this talk, we improve this inequality for the case of bridge sphere in the 3-shpere $S^3$. In fact, we show the following: Suppose that $K$ is in a minimal bridge position with a bridge sphere $P$. If $d(P, K)>|P∩K|-2$, then $K$ has a unique minimal bridge position.