On keen Heegaard splittings

Abstract

In this paper, we introduce a new concept of {\it strongly keen} for Heegaard splittings, and show that, for any integers $n\ge 2$ and $g\ge 3$, there exists a strongly keen Heegaard splitting of genus $g$ whose Hempel distance is $n$.

arXiv admin note: text overlap with arXiv:1210.7627