## Event Date:

## Event Location:

- 4607B South Hall

Joint work with Yeonhee Jang (Nara Women's Univ.) and Tsuyoshi Kobayashi (Nara Women's Univ.) Hempel introduced the concept of distance of Heegaard splitting by using curve complex, and showed that there exist Heegaard splittings of closed orientable 3-manifolds with distance $>n$ for any integer $n$. In this talk, we construct pairs of curves with distance exactly $n$ for any integer $n$. Then we apply the result to show the followings: (1) there exist Heegaard splittings (of 3-manifolds with two boundary components) with distance exactly $n$. (2) for each $g(>1)$, there exists a constant $N_g$ such that for each $n>N_g$ there exist genus-$g$ Heegaard splittings of closed 3-manifolds with distance exactly $n$.