Yeonhee Jang

Heegaard splittings of distance exactly n

In this paper, we show that, for any integers

Meridional rank and bridge number for a class of links

n\geq 2

A KNOT WITH DESTABILIZED BRIDGE SPHERES OF ARBITRARILY HIGH BRIDGE NUMBER

and

DISTANCE OF BRIDGE SURFACES FOR LINKS WITH ESSENTIAL MERIDIONAL SPHERES

g\geq 2

On keen Heegaard splittings

, there exist genus-

Classification of 3-bridge spheres of 3-bridge arborescent links

g

Meridional rank of knots whose exterior is a graph manifold

Heegaard splittings of compact 3-manifolds with distance exactly

Bridge splittings of links with distance exactly n

n

(1,1)-BRIDGE SPLITTINGS WITH DISTANCE EXECTLY

.

n

We prove that links with meridional rank 3 whose 2-fold branched covers are graph manifolds are 3-bridge links. This gives a partial answer to a question by S. Cappell and J. Shaneson on the relation between the bridge numbers and meridional ranks of links. To prove this, we also show that the meridional rank of any satellite knot is at least 4.