Name Ayako Ido Nara Women's University Session Jan 9 17:10~17:30 E11-101 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. 101-1-9/AyakaIdo.pdf