Jesse Johnson

Flipping bridge surfaces and bounds on the stable bridge number

We show that if K is a knot in S 3 and U is a bridge sphere for K with high distance and 2n punctures, the number of perturbations of K required to interchange the two balls bounded by U via an isotopy is n. We also construct a knot with two different bridge spheres with 2n and 2n 1 bridges respectively for which any common perturbation has at least 3n 4 bridges. We generalize both of these results to bridge surfaces for knots in any 3‐manifold. 57M25, 57M27, 57M50

Bridge distance and plat projections

We calculate the bridge distance for

Mapping class groups of medium distance Heegaard splittings

m

Neighbors of Knots in the Gordian Graph

-bridge knots/links in the

The coarse geometry of the Kakimizu complex

3

HEEGAARD SPLITTINGS WITH LARGE SUBSURFACE DISTANCES

-sphere with sufficiently complicated

Bounds for the genus of a normal surface

2m

On the existence of high index topologically minimal surfaces

-plat projections. In particular we show that if the underlying braid of the plat has

FLIPPING AND STABILIZING HEEGAARD SPLITTINGS

n - 1

Bridge Number and the Curve Complex

rows of twists and all its exponents have absolute value greater than or equal to three then the distance of the bridge sphere is exactly