分野別セミナー

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 $2−(Q\K)$. 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 $d(P, K) > |P¥capK
| − 2$, then $K$ has a unique minimal bridge position.