The Kakimizu complex is simply connected
Destabilizing amalgamated Heegaard splittings , with Richard Weidmann
Thin position of knots and 3-manifolds , with Hugh Howards
On the geometric and algebraic rank of graph manifolds , with Richard Weidmann
Pdf-files of recent publications:
Heegaard genus formula for Haken manifolds
3-manifolds with planar presentations and the width of satellite knots , with Marty Scharlemann
Heegaard splittings of graph manifolds
Additivity of Bridge Numbers of Knots
Genus 2 hyperbolic 3-manifolds of arbitrarily large volume
Comparing Heegaard and JSJ structures or orientable 3-manifolds , with Marty Scharlemann
Annuli in generalized Heegaard splittings and degeneration of tunnel number , with Marty Scharlemann
The tunnel number of the sum of n knots is at least n , with Marty Scharlemann
Tunnel numbers of small knots do not go down under connected sum , with Kanji Morimoto
Additivity of tunnel number for small knots
The stabilization problem for Heegaard splittings of Seifert fibered spaces
Weakly reducible Heegaard splittings of Seifert fibered spaces
Irreducible Heegaard splittings of Seifert fibered spaces are either vertical or horizontal , with Yoav Moriah
Heegaard splittings of Seifert fibered spaces with boundary
The classification of Heegaard splittings for (compact orientable surface) x circle
Here are a few older manuscripts that are educational. I don't currently intend to publish these, for a variety of reasons. Of course, I could change my mind.
Waldhausen's "Heegaardzerlegungen der 3-Sphaere"
(This is an annotated and illustrated translation, written for the benefit of local graduate students. I recently noticed that S. Schleimer has something along these lines as well.)
Amalgamations of Heegaard splittings are unique
(This is addressed elsewhere, for instance by D. Bachman and M. Lackenby. The result seems kind of obvious, but there is an issue here.)
Below is a very coarse set of notes that I compiled for a course on 3-manifolds. Much of my lecturing time was spent drawing appropriate pictures. I hope to substantially revise these notes and add the pictures sometime in the future.
Sketchy notes for a class on 3-manifolds
If you have any questions or comments, send mail to jcs at math dot ucdavis dot edu.