Jennifer Schultens

Additivity of bridge numbers of knots

We provide a new proof of the following results of H. Schubert: if

THE TUNNEL NUMBER OF THE SUM OF n KNOTS IS AT LEAST n

K

Lecture Notes on Generalized Heegaard Splittings

is a satellite knot with companion

Annuli in generalized Heegaard splittings and degeneration of tunnel number

J

3-manifolds with planar presentations and the width of satellite knots

and pattern

The stabilization problem for Heegaard splittings of Seifert fibered spaces

(\skew1\hat{V}, L)

Destabilizing amalgamated Heegaard splittings

with index

Tunnel numbers of small knots do not go down under connected sum

k

Bridge numbers of torus knots

, then the bridge numbers satisfy the following:

Contractibility of the Kakimizu complex and symmetric Seifert surfaces

b(K) \geq k \cdot (b(J))