Name  Ayako Ido 

Affiliation  Nara Women's University 
Talk type  Session 
Time  Jan 9 17:10~17:30 
Location  E11101 
Title  On the distance of bridge spheres for knots 
Abstract 
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 3manifold, Tomova shows that either two bridge surfaces $P$, $Q$ for $K$ are equivalent or the distance $d(P, K)$ is at most $2χ(QK)$. In this talk, we improve this inequality for the case of bridge sphere in the 3shpere $S^3$. In fact, we show the following: Suppose that $K$ is in a minimal bridge position with a bridge sphere $P$. If $d(P, K)>P∩K2$, then $K$ has a unique minimal bridge position.

Slide  10119/AyakaIdo.pdf 